Pump (Centrifugal, Slurry)

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Description

The article describes a method for estimating the performance of a centrifugal slurry pump.

Centrifugal pumps are a critical component of metallurgical processing plants. The transport of solid particles in slurries presents additional complexity, as pumps are typically tested and rated for water duties only.

The centrifugal slurry pump modelling approach described below has the following features:

  • The reduction of typical vendor pump performance curves into generalised mathematical relationships for computational implementation
  • The de-rating of water duty pump performance for heterogenous slurries
  • Estimation of the effects of elevation, piping system properties and transport destination processing equipment (e.g. hydrocyclones)
  • An estimation of the settling velocity of slurries during transport

Note that the centrifugal slurry pump model described here is not intended to replace the more comprehensive design methods and tools currently available. Rather, it is intended to provide the user with a comparatively simpler tool which can be integrated with other unit models and provide useful estimates of pump speed, flow rate, motor power, and pressure head in the broader context of a mineral processing circuit. More sophisticated methods should be applied for engineering design or optimisation.

Model theory

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Generalised characteristic curves

Speed

Efficiency

Total dynamic head

Friction factor

Head ratio

Cave method

Warman method

Weir / HI method

Efficiency ratio

Motor Power

Froth Volume Factor

Settling velocity

Pumps in series and parallel

Excel

The centrifugal slurry pump model may be invoked from the Excel formula bar with the following function call: 

=mdUnit_Pump_King(Parameters as Range)

Invoking the function with no arguments will print Help text associated with the model, including a link to this page.

The Parameters array and model results are defined below in matrix notation, along with example images showing the same arrays in the Excel interface:

[math]\displaystyle{ Parameters= \begin{bmatrix} n_{\rm stages}\\ n_{\rm parallel}\\ \text{Model mode}\\ \text{f method}\\ \text{HR method}\\ \text{ER method}\\ \text{FL method}\\ D_{\rm imp}\text{ (m)}\\ A_{\rm N}\\ B_{\rm N}\\ C_{\rm N}\\ A_{\rm E}\\ B_{\rm E}\\ C_{\rm E}\\ (Q_{\rm M})_{\rm S}\text{ (kg/s)}\\ (Q_{\rm M})_{\rm L}\text{ (kg/s)}\\ \rho_{\rm S}\text{ (t/m}^\text{3}\text{)}\\ \rho_{\rm L}\text{ (t/m}^\text{3}\text{)}\\ d_{50}\text{ (m)}\\ {\rm FVF}\text{ (v/v)}\\ \mu\text{ (Pa.s)}\\ H_{\rm s}\text{ (m)}\\ D\text{ (m)}\\ L\text{ (m)}\\ k\text{ (m)}\\ H_{\rm e}\text{ (kPa)}\\ \eta\text{ (kW/kW)}\\ N\text{ (Hz)}\\ f\\ {\rm HR}\text{ (m/m)}\\ {\rm ER}\text{ (kW/kW)}\\ F_{\rm L}\\ C_{\rm fp}\text{ (frac)}\\ \end{bmatrix},\;\;\;\;\;\; \mathit{mdUnit\_Pump\_King} = \begin{bmatrix} \text{Iterations}\\ Q_{\rm Feed}\text{ (m}^3\text{/s)}\\ Q\text{ (m}^3\text{/s)}\\ \rho_{\rm SL}\text{ (t/m}^3\text{)}\\ C_{\rm W}\text{ (w/w)}\\ C_{\rm V}\text{ (v/v)}\\ F_{\rm L}\\ V_{\rm L}\text{ (m/s)}\\ V\text{ (m/s)}\\ \mathrm {Re}\\ f\\ H_{\rm f}\text{ (m)}\\ H_{\rm e}\text{ (m)}\\ H_{\rm t}\text{ (m)}\\ {\rm HR}\text{ (m/m)}\\ H_{\rm w}\text{ (m)}\\ N\text{ (Hz)}\\ N_{\rm pu}\\ N_{\rm Q}\\ E\text{ (kW/kW)}\\ {\rm ER}\text{(kW/kW)}\\ P_{\rm shaft}\text{ (kW)}\\ P_{\rm motor}\text{ (kW)}\\ \end{bmatrix}\;\;\;\;\;\; }[/math]


where:

  • [math]\displaystyle{ \text{Model mode} }[/math] indicates whether the pump model returns the flow rate at a given speed or the speed at a given flow rate, where
    0 = Calculate speed at flow rate, 1 = Calculate flow rate at speed
  • [math]\displaystyle{ \text{f method} }[/math] is the friction factor estimation method, 0 = User, 1 = Colebrook, 2 = Churchill
  • [math]\displaystyle{ \text{HR method} }[/math] is the head ratio estimation method, 0 = User, 1 = Cave, 2 = Warman, 3 = Weir / HI
  • [math]\displaystyle{ \text{ER method} }[/math] is the efficiency ratio estimation method, 0 = User, 1 = ER equals HR, 2 = Warman, 3 = Weir / HI
  • [math]\displaystyle{ \text{FL method} }[/math] is the Durand factor estimation method, 0 = User, 1 = Equation
  • [math]\displaystyle{ (Q_{\rm M})_{\rm S} }[/math] is the mass flow rate of solids through the pump (kg/s)
  • [math]\displaystyle{ (Q_{\rm M})_{\rm L} }[/math] is the mass flow rate of liquids through the pump (kg/s)
  • [math]\displaystyle{ \text{Iterations} }[/math] is the number of internal model iterations required to resolve any dependence between friction head and pump flow rate
  • [math]\displaystyle{ Q_{\rm Feed} }[/math] is the actual volumetric flow rate of slurry in the pump feed, computed from [math]\displaystyle{ (Q_{\rm M})_{\rm S} }[/math], [math]\displaystyle{ (Q_{\rm M})_{\rm L} }[/math], [math]\displaystyle{ \rho_{\rm S} }[/math], and [math]\displaystyle{ \rho_{\rm L} }[/math]
Figure 4. Example showing the selection of the Parameters (blue frame) array in Excel.
Figure 5. Example showing the Results (light blue frame) array in Excel.

When calculating speed at flow rate ([math]\displaystyle{ \text{Model mode} = 0 }[/math]):

  • [math]\displaystyle{ Q = Q_{\rm Feed} }[/math] and the value of [math]\displaystyle{ N }[/math] is computed by the model and returned.
  • This mode might be used to simulate the operating point of a variable speed pump in a steady state model, for example.

When calculating flow rate at speed ([math]\displaystyle{ \text{Model mode} = 1 }[/math]):

  • [math]\displaystyle{ N }[/math] is a user input and [math]\displaystyle{ Q }[/math] is computed and returned.
  • The return value of [math]\displaystyle{ Q }[/math] may be different to [math]\displaystyle{ Q_{\rm Feed} }[/math].
  • This might indicate a quantity of make-up water is required to maintain the level of a tank feeding the pump, for example.

SysCAD

The sections and variable names used in the SysCAD interface are described in detail in the following tables.

MD_Pump page

The first tab page in the access window will have this name.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
Tag Display This name tag may be modified with the change tag option.
Condition Display OK if no errors/warnings, otherwise lists errors/warnings.
ConditionCount Display The current number of errors/warnings. If condition is OK, returns 0.
GeneralDescription / GenDesc Display This is an automatically generated description for the unit. If the user has entered text in the 'EqpDesc' field on the Info tab (see below), this will be displayed here.

If this field is blank, then SysCAD will display the unit class ID.

Requirements
On CheckBox This enables the unit. If this box is not checked, then no model calculations or actions are performed.
Options
ShowQIn CheckBox QIn and associated tab pages (eg Sp) will become visible, showing the properties of the combined feed stream.
ShowQOut CheckBox QOut and associated tab pages (eg Sp) will become visible, showing the properties of the overflow stream.
SizeForPassingFracCalc Input Size fraction for % Passing calculation. The size fraction input here will be shown in the Stream Summary section.
FracForPassingSizeCalc Input Fraction passing for Size calculation. The fraction input here will be shown in the Stream Summary section.
Stream Summary
MassFlow / Qm Display The total mass flow in each stream.
SolidMassFlow / SQm Display The Solids mass flow in each stream.
LiquidMassFlow / LQm Display The Liquid mass flow in each stream.
VolFlow / Qv Display The total Volume flow in each stream.
Temperature / T Display The Temperature of each stream.
Density / Rho Display The Density of each stream.
SolidFrac / Sf Display The Solid Fraction in each stream.
LiquidFrac / Lf Display The Liquid Fraction in each stream.
Passing Display The mass fraction passing the user-specified size (in the field SizeForPassingFracCalc) in each stream.
Passes Display The user-specified (in the field FracForPassesSizeCalc) fraction of material in each stream will pass this size fraction.

Pump page

The Pump page is used to specify the input parameters for the centrifugal slurry pump model.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
Pump
HelpLink ButtonModelHelp.png Opens a link to this page using the system default web browser. Note: Internet access is required.
Iterations Display Shows the number of internal model iterations (per SysCAD step) required to converge the pump model.
Duty
NumStages Input The number of sequential duplicate pump stages.
NumParallel Input The number of duplicate pumps in parallel.
Config
CalculationMode Speed The model calculates the speed required to pump the volumetric flow rate of the feed stream, at the given head.
Flow Rate The model calculates the pump flow rate at the user-specified speed and head.
CharacteristicCurve
ImpellerDiameter / Dimp Input Diameter of the pump impeller.
AN Input Coefficient of the generalised characteristic curve equation.
BN Input Coefficient of the generalised characteristic curve equation.
CN Input Coefficient of the generalised characteristic curve equation.
EfficiencyCurve
AE Input Coefficient of the generalised efficiency curve equation.
BE Input Coefficient of the generalised efficiency curve equation.
CE Input Coefficient of the generalised efficiency curve equation.
Feed
FrothVolumeFactor / FVF Input Value of the Froth Volume Factor.
VolFlow / Qv Display Volumetric flow of solids and liquids in the pump feed stream, adjusted by the Froth Volume Factor.
SolidDensity / SRho Display Density of solids in the pump feed stream.
Liquids / LRho Display Density of liquids in the pump feed stream.
SlurryDensity / SLRho Display Density of slurry (solids plus liquids) in the pump feed stream.
SolidFrac / Sf Display Mass fraction of solids in the feed stream.
SolidVolFrac / Svf Display Volume fraction of solids in the feed stream.
LViscosity Display Viscosity of liquids in the feed stream.
Userd50 CheckBox Indicates user-specified d50 value. Default is to use d50 computed from the feed stream.
d50 Input/Display Mean size of particles in pump feed.
Head
StaticHead
StaticHead / Hs Input Static head component of the total dynamic head.
FrictionHead
Method User Defined The friction factor is specified by the user.
Colebrook The Colebrook equation is used to estimate the friction factor.
Churchill The Churchill equation is used to estimate the friction factor.
PipeDiameter / D Input Internal diameter of the pipe
EquivPipeLength / L Input Equivalent length of the pipe, including pipe fittings etc.
FrictionFactor / f Input / Display Friction factor used to estimate friction head.
Roughness / k Input Absolute surface roughness of the pipe internal wall.
ReynoldsNumber / Re Display Reynolds Number of the pipe flow stream.
FrictionHead / Hf Display Friction head component of the total dynamic head.
EquipmentHead
EquipmentPressure / Pe Input Pressure drop due to equipment at the end of the pipe.
EquipmentHead / He Display Pressure drop due to equipment at the end of the pipe, converted to head measurement units.
Total head
TotalHead / Ht Display Total dynamic head that the pump acts against. Sum of static, friction and equipment heads.
HeadRatio
Method User Defined The head ratio is specified by the user.
Cave Cave's method is used to estimate the head ratio.
Warman The Warman method is used to estimate the head ratio.
Weir / HI The Weir / HI method is used to estimate the head ratio.
HeadRatio / HR Input / Display Head ratio of the slurry stream.
EquivWaterHead / Hw Display Head of water equivalent to the slurry total dynamic head, as estimated via the head ratio.
EfficiencyRatio
Method User Defined The efficiency ratio is specified by the user.
Equals HR The efficiency ratio is set equal to the value of the head ratio.
Warman The Warman method is used to estimate the efficiency ratio.
Weir / HI The Weir / HI method is used to estimate the efficiency ratio.
EfficiencyRatio / ER Input / Display Efficiency ratio of the slurry stream.
SettlingVelocity
Method User Defined The Durand factor is specified by the user.
Durand The Durand factor is estimated by the Durand equation.
DurandFactor / FL Input / Display Durand factor to be used in the Durand equation.
SettlingVelocity / VL Display Settling velocity estimated by the Durand equation.
PipeVelocity / V Display Velocity of flow through the pipe at pump flow rate, Q.
Speed
Iterations Display The number of internal model iterations required to resolve any dependence between friction head and pump flow rate.

Only applicable when CalculationMode = Flow Rate.

N Input / Display Rotational speed of the pump.
Q Display Volumetric flow rate of the pump at the given speed and head.
HeadNumber / NPU Display Dimensionless pump head number used in calculations.
FlowNumber / NQ Display Dimensionless pump flow number used in calculations.
Power
MotorFactor / Eta Input Efficiency factor of the pump. Fraction of power input to the motor which is useable by the pump at the shaft to move fluid.
Efficiency / E Display Efficiency of the pump.
ShaftPower / PShaft Display Power drawn by the pump at the shaft.
MotorPower / PMotor Display Power drawn by the pump motor, including inefficiencies.

CSz page

The CSz page provides composition and constituent information by particle size for QIn and QOut. It appears after the standard SysCAD stream information when the corresponding stream display option is selected.

  • Results are available for Species, Component, Element, and Individual Phase, with views for Composition, Distribution by Size, and Stream Contribution.
  • The calculations are described in Stream Analyser - Composition by Size.
  • These combined composition-by-size results are not available in the standard SysCAD stream pages. They are particularly useful for comparing simulated results with measured size-by-size data, such as elemental assays or mineral grades by size.
Tag (Long/Short) Input / Display Description/Calculated Variables/Options
Distribution
Name Display Shows the name of the SysCAD Size Distribution (PSD) quality associated with the feed stream.
IntervalCount Display Shows the number of size intervals in the SysCAD Size Distribution (PSD) quality associated with the feed stream.
SpWithPSDCount Display Shows the number of species in the feed stream assigned with the SysCAD Size Distribution (PSD) quality.
CSz
Property Composition Displays the mass fraction of each species, component, element, or individual phase within each size interval. The All row displays the overall composition over all size intervals.
Distribution by Size Displays the fraction of each constituent's total mass that occurs in each size interval. The All column displays the distribution by size of all solids with a particle size distribution property in the selected stream.
Stream Contribution Displays each constituent and size interval mass as a fraction of the total mass of all solids with a particle size distribution property in the selected stream.
Comp
Size Display Size of each interval in the mesh series.
All (All column) Display Total composition of all solids with a particle size distribution property in each size interval. The result is 100% when the interval contains solids with a particle size distribution property and 0 when it does not.
Comp Display Mass fraction of each solid species with a particle size distribution property within each size interval.
All (All row, All column) Display Total composition of all solids with a particle size distribution property over all size intervals. The result is 100% when the selected stream contains solids with a particle size distribution property and 0 when it does not.
All (All row, per species) Display Overall mass fraction of each solid species with a particle size distribution property in the selected stream for all size intervals.
CmpComp
Components
ButtonHideComponents.png
ButtonShowComponents.png
 Hides or shows the component composition table.
Size Display Size of each interval in the mesh series.
All (All column) Display Total composition of all solids with a particle size distribution property in each size interval. The result is 100% when the interval contains solids with a particle size distribution property and 0 when it does not.
CmpComp Display Mass fraction of each displayed solid component within each size interval.
All (All row, All column) Display Total composition of all solids with a particle size distribution property over all size intervals.
All (All row, per component) Display Overall mass fraction of each displayed solid component in the selected stream over all size intervals.
EleComp
Elements
ButtonHideElements.png
ButtonShowElements.png
 Hides or shows the element composition table.
Size Display Size of each interval in the mesh series.
All (All column) Display Total composition of all solids with a particle size distribution property in each size interval. The result is 100% when the interval contains solids with a particle size distribution property and 0 when it does not.
EleComp Display Mass fraction of each displayed element within each size interval.
All (All row, All column) Display Total composition of all solids with a particle size distribution property over all size intervals.
All (All row, per element) Display Overall mass fraction of each displayed element in the selected stream over all size intervals.
IPhComp
IPhases
ButtonHideIPhases.png
ButtonShowIPhases.png
 Hides or shows the individual phase composition table.
Size Display Size of each interval in the mesh series.
All (All column) Display Total composition of all solids with a particle size distribution property in each size interval. The result is 100% when the interval contains solids with a particle size distribution property and 0 when it does not.
IPhComp Display Mass fraction of each displayed individual phase within each size interval.
All (All row, All column) Display Total composition of all solids with a particle size distribution property over all size intervals.
All (All row, per individual phase) Display Overall mass fraction of each displayed individual phase in the selected stream over all size intervals.
Dist
Size Display Size of each interval in the mesh series.
All (All column) Display Fraction of the total mass of all solids with a particle size distribution property in the selected stream that occurs in each size interval.
Dist Display Fraction of the total mass of each solid species with a particle size distribution property that occurs in each size interval.
All (All row, All column) Display Total distribution by size of all solids with a particle size distribution property. The result is 100% when the selected stream contains solids with a particle size distribution property and 0 when it does not.
All (All row, per species) Display Total distribution by size of each solid species with a particle size distribution property. The result is 100% when that species is present and 0 when it is not.
CmpDist
Components
ButtonHideComponents.png
ButtonShowComponents.png
 Hides or shows the component distribution-by-size table.
Size Display Size of each interval in the mesh series.
All (All column) Display Fraction of the total mass of all solids with a particle size distribution property in the selected stream that occurs in each size interval.
CmpDist Display Fraction of each displayed solid component's total mass that occurs in each size interval.
All (All row, All column) Display Total distribution by size of all solids with a particle size distribution property.
All (All row, per component) Display Total distribution by size of each displayed solid component. The result is 100% when that component is present and 0 when it is not.
EleDist
Elements
ButtonHideElements.png
ButtonShowElements.png
 Hides or shows the element distribution-by-size table.
Size Display Size of each interval in the mesh series.
All (All column) Display Fraction of the total mass of all solids with a particle size distribution property in the selected stream that occurs in each size interval.
EleDist Display Fraction of each displayed element's total mass that occurs in each size interval.
All (All row, All column) Display Total distribution by size of all solids with a particle size distribution property.
All (All row, per element) Display Total distribution by size of each displayed element. The result is 100% when that element is present and 0 when it is not.
IPhDist
IPhases
ButtonHideIPhases.png
ButtonShowIPhases.png
 Hides or shows the individual phase distribution-by-size table.
Size Display Size of each interval in the mesh series.
All (All column) Display Fraction of the total mass of all solids with a particle size distribution property in the selected stream that occurs in each size interval.
IPhDist Display Fraction of each displayed individual phase's total mass that occurs in each size interval.
All (All row, All column) Display Total distribution by size of all solids with a particle size distribution property.
All (All row, per individual phase) Display Total distribution by size of each displayed individual phase. The result is 100% when that individual phase is present and 0 when it is not.
Contr
Size Display Size of each interval in the mesh series.
All (All column) Display Fraction of the total mass of all solids with a particle size distribution property in the selected stream that occurs in each size interval.
Contr Display Stream Contribution of each solid species with a particle size distribution property and size interval to the total mass of all solids with a particle size distribution property in the selected stream.
All (All row, All column) Display Total stream contribution of all solids with a particle size distribution property. The result is 100% when the selected stream contains solids with a particle size distribution property and 0 when it does not.
All (All row, per species) Display Overall stream contribution of each solid species with a particle size distribution property for all size intervals.
CmpContr
Components
ButtonHideComponents.png
ButtonShowComponents.png
 Hides or shows the component stream contribution table.
Size Display Size of each interval in the mesh series.
All (All column) Display Fraction of the total mass of all solids with a particle size distribution property in the selected stream that occurs in each size interval.
CmpContr Display Stream Contribution of each displayed solid component and size interval to the total mass of all solids with a particle size distribution property in the selected stream.
All (All row, All column) Display Total stream contribution of all solids with a particle size distribution property.
All (All row, per component) Display Overall stream contribution of each displayed solid component for all size intervals.
EleContr
Elements
ButtonHideElements.png
ButtonShowElements.png
 Hides or shows the element stream contribution table.
Size Display Size of each interval in the mesh series.
All (All column) Display Fraction of the total mass of all solids with a particle size distribution property in the selected stream that occurs in each size interval.
EleContr Display Stream Contribution of each displayed element and size interval to the total mass of all solids with a particle size distribution property in the selected stream.
All (All row, All column) Display Total stream contribution of all solids with a particle size distribution property.
All (All row, per element) Display Overall stream contribution of each displayed element for all size intervals.
IPhContr
IPhases
ButtonHideIPhases.png
ButtonShowIPhases.png
 Hides or shows the individual phase stream contribution table.
Size Display Size of each interval in the mesh series.
All (All column) Display Fraction of the total mass of all solids with a particle size distribution property in the selected stream that occurs in each size interval.
IPhContr Display Stream Contribution of each displayed individual phase and size interval to the total mass of all solids with a particle size distribution property in the selected stream.
All (All row, All column) Display Total stream contribution of all solids with a particle size distribution property.
All (All row, per individual phase) Display Overall stream contribution of each displayed individual phase for all size intervals.

About page

This page is provides product and licensing information about the Met Dynamics Models SysCAD Add-On.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
About
HelpLink ButtonLicensingHelp.png Opens a link to the Installation and Licensing page using the system default web browser. Note: Internet access is required.
Information ButtonCopyToClipboard.png Copies Product and License information to the Windows clipboard.
Product
Name Display Met Dynamics software product name
Version Display Met Dynamics software product version number.
BuildDate Display Build date and time of the Met Dynamics Models SysCAD Add-On.
License
File ButtonBrowse.png This is used to locate a Met Dynamics software license file.
Location Display Type of Met Dynamics software license or file name and path of license file.
SiteCode Display Unique machine identifier for license authorisation.
ReqdAuth Display Authorisation level required, MD-SysCAD Full or MD-SysCAD Runtime.
Status Display License status, LICENSE_OK indicates a valid license, other messages report licensing errors.
IssuedTo Display Only visible if Met Dynamics license file is used. Name of organisation/seat the license is authorised to.
ExpiryDate Display Only visible if Met Dynamics license file is used. License expiry date.
DaysLeft Display Only visible if Met Dynamics license file is used. Days left before the license expires.

External links

References

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