## How to size a slurry pump

Contents

SOME DEFINITIONS. 1

DATA REQUIRED.. 1

SELECTING THE APPROPRIATE PUMP. 1

Step 01.       DETERMINE THE FLOW RATE......................................................................... 1

Step 02.       DETERMINE THE STATIC HEAD...................................................................... 2

Step 03.       DETERMINE THE PUMP HEAD & EFFICIENCY CORRECTIONS.. 2

Step 04.       DETERMINATION OF LIMITING SETTLING VELOCITY......................3

Step 05.       DETERMINE THE PIPE DIAMETER............................................................... 4

Step 06.       CALCULATE THE TOTAL HEAD LOSS........................................................... 5

Step 07.       CALCULATE THE TOTAL DYNAMIC HEAD.................................................. 7

Step 08.        EQUIVALENT WATER TOTAL DYNAMIC HEAD...................................... 7

Step 09.       SELECTION OF PUMP TYPE AND MATERIALS...................................... 8

Step 10.       PUMP SELECTION.................................................................................................. 18

SELECTION CHART FOR CENTRIFUGAL PUMPS......................................................... 18

PERFORMANCE CURVE CHART.............................................................................................. 19

Step 11.       CALCULATION OF POWER OF PUMP........................................................... 22

NOMENCLATURE  ........................................................................................................................... 22

SOME DEFINITIONS

• TPH (Tonnes of Solids to be Pumped): Weight of dry solids to be pumped per hour. Units are tph (tonnes per hour).
• Hs (Static Lift): This is the vertical height through which the slurry is to be raised. For our purposes, it is suitable to take the level difference from the pump to the discharge point.
• Size of Solids: The d50 sizing of the particles to be pumped.
• Pipe Equivalent Length (Leq): This is the actual length of pipe installed plus the total equivalent length of all fittings.

Leq = Straight pipe length + equivalent length of all pipe fittings.

• Pipe Material: The various references list a wide range of materials from which pipe is made. Experience once again shows that in most plants, the slurry is pumped through polyethylene, bare steel pipe or rubber lined steel pipe.

DATA REQUIRED

In most average plant situations, the Process design will require that a specific tonnage rate of solids be transported from a hopper, to a point at a level and distance away from the pump site. The transport medium is water at near ambient temperature. The process will most probably dictate that the slurry must be pumped at a certain pulp density. Thus, the required input data is:

• G. Slurry (Sm)
• G. Solids (S)
• TPH of dry solids to be pumped (tph)
• Solids size (d50)
• Pipe Material internal roughness (k)

SELECTING THE APPROPRIATE PUMP

Step 01.                   DETERMINE THE FLOW RATE

The flow rate can be evaluated in numerous ways, but is usually established by the volume of solids to be pumped and the proposed concentration of solids and liquid.

• Concentration of solids by volume

• Concentration of solids by weight

• Volume flow rate of slurry (m3/hr)

Step 01.                   DETERMINE THE STATIC HEAD

The static head (vertical height on both the intake and discharge side of the pump) must be established, and the difference calculated to determine the net static head to be overcome by the pump.

The total static head can be calculated by taking eye of impeller of pump as datum.

Note: Total static head is usually positive but total Suction head may be positive, or negative.

Step 03.                   DETERMINE THE PUMP HEAD & EFFICIENCY CORRECTIONS

It is also necessary to determine the effect of the slurry on the performance of the pump. It will be necessary to know:

1. a) The average particle size, d50, of the solids to be pumped
2. b) The concentration of solids by weight (Cw), and
3. c) The dry SG of the solids (S).

These three values can now be entered into the nomograph shown in Figure (a), to determine the Head and Efficiency correcting ratio (HR and ER).

The pump head ratio (HR) is the ratio of slurry head produced to the head produced for water at the pump best-efficiency point (BEP) measured for water.

The pump efficiency ratio (ER) is the ratio of slurry efficiency to the efficiency for water at the pump BEP measured for water.

Efficiency Ratio,

Figure (a) has been developed, from test and field results, to enable a reasonable estimation of HR and ER in most practical cases.

Figure (a): Performance of centrifugal pumps on slurry

Note: This chart applies to simple mixtures of solids and water only.

Step 01.                   DETERMINATION OF LIMITING SETTLING VELOCITY

Limiting settling velocity can be calculated using Durand Formula:

Where, the parameter FL is dependent upon particle sizing and solids concentration.

Figure (b) represents the results of field tests on slurries of widely-graded sizing.

The particle sizing is simply expressed by the d50 term.

Note: FL increases with increasing Cv to about Cv = 30%, and beyond Cv = 30%, FL decreases with increasing Cv due to increasing interference of particles with each other.

Figure (b): Modified Durand’s limiting settling velocity parameter

(For particles of widely graded sizing)

Step 01.                   DETERMINE THE PIPE DIAMETER

The selection of the optimum pipe diameter is also of critical importance in any slurry pumping system. The use of a pipe that is too small can result in either insufficient flow rate or excessively high power requirements.

First, we choose a trial pipe internal diameter.

Note: If a pipe diameter has not been specified, the best way to arrive at one is to select the first pipe size giving a velocity above 3 m/s. This pipe size should be checked to ensure that the actual velocity is greater than the limiting settling velocity.

Velocity of slurry can be calculated as

• Case 1 : If v ≥ vL, the velocity available is sufficient to maintain the solids in suspension, pipe is selected.
• Case 2: If v < vL, the velocity available is insufficient to maintain the solids in suspension and solid particles will progressively settle within the pipe, ultimately causing a total blockage of the pipe. Hence, the exercise is repeated for one size smaller pipe diameter so that the greater velocity is available to ensure that settling does not occur.

Step 01.                   CALCULATE THE TOTAL HEAD LOSS

When slurry flows through the pipe, it experiences some resistance due to which the flow loses some of its energy. The head loss is broadly classified into major and minor losses.

Slurry passing through a pipeline creates friction (or drag), against the pipe walls. The longer the pipeline, the greater the friction forces to be overcome by the slurry pump. Prior to any pump selection, it is therefore imperative that the actual length of the pipeline and details of any bends or other pipe variations be established, as accurately as possible.

Friction head loss can now be calculated by using Darcy’s formula:

Calculation of f

• Renold’s Number

• Swamee Jain Friction Factor

Here, k is the pipe internal surface roughness measured in meters in SI system.

Alternatively, Darcy Friction Factor, f can be calculated by using Warman Pipe Friction Chart shown in figure (c).

NOTE: For convenience, this chart is entered at values of Inside Diameter of Pipe: expressed in mm.

All the energy losses which are quite small in comparison with the energy losses due to friction come under minor head loss. These occur in the flowing fluid due to change in velocity of the flowing fluid.

Some of the minor head losses are:

a ) Loss at inlet to suction pipe

b)Loss at exit (pipe discharge)

c) Head Losses due to Contractions and Enlargements

These additional head losses are calculated by the use of formula provided in figure (d).

d) Loss of energy in various pipe fittings

e) Loss of energy in bends

Note: Here, v is used to indicate the upstream velocity and v1 is used for downstream velocity.

Step 07.                   CALCULATE THE TOTAL DYNAMIC HEAD

 Total Dynamic Head (Hm) = Total static head (Hd+Hs)+ Total head Loss () (m. of slurry mixture)

This is the Total Dynamic Head calculated in terms of m. of slurry mixture.

Step 08.                 EQUIVALENT WATER TOTAL DYNAMIC HEAD

By using the head ratio (HR) from figure (a), we are able to convert the calculated slurry total dynamic head to the equivalent water total dynamic head.

This is the Total Dynamic Head calculated in terms of m. of water.

Step 09.                   SELECTION OF PUMP TYPE AND MATERIALS

Prior to the selection of a specific pump size, it is necessary to determine the pump type and material required.

Now we have to select the right type of pump by considering the operating costs, taking into account wear, maintenance and energy. Depending on the application it can be a horizontal, vertical or submersible Slurry Pump. It can also be a pump for extreme, heavy or normal wear conditions.

Selection of the type of materials to be used for slurry pumping applications is not a precise procedure. The procedure must first account for all the factors (variable characteristics) of the particular slurry.

The choice of wear parts is a balance between resistance to wear and cost of wear parts. There are two strategies for resisting wear:

The wear material has to be hard to resist cutting action of impinging solids!

OR

The wear material has to be elastic to be able to absorb the shocks and rebound of particles!

The basic parameters required to make a selection of the type of material is:

1. The particle sizing of the solids to be pumped,
2. The shape and hardness of these solids,
3. The corrosive properties of the “liquid” component of the slurry to be pumped (temperature, pH and chemicals), and
4. Impeller speed

Table (1): Classification of pumps according to solid particle size (sand hardness particles)

The material selection for the pump liners and impellers is made from two basic types of materials:

1. Wear/erosion resistant cast alloys

Metal is generally more tolerant to abuse than rubber and is the best choice for coarse material. Wear resistant cast alloys are used for slurry pump liners and impellers where conditions are not suited to rubber, such as with coarse or sharp edged particles, or on duties having high impeller peripheral velocities or high operating temperatures.

1. Elastomers

Elastomers are normally rubber in various qualities or polyurethane. Natural rubber is by far the major elastomers in slurry pumping and is the most cost effective for fine solids. Generally, depending on their sharpness and density, particle sizes of up to 5-8 mm can be pumped.

But, remember that oversize scrap and sharp particles can destroy the wear parts, especially the impeller.

Polyurethane is available for most pump ranges and offers excellent wear resistance for finer particles (< 0.15 mm), but is less sensitive to oversized scrap than rubber. It has its peak performance in low angular impact and sliding wear.

For slurry pumps, impellers are generally constructed in hard metal alloys or metal reinforced elastomers.

Let us look at different types of material used by Warman. A major advantage of the Warman slurry pump is the number of optional materials available. This enables a pump to be constructed with the most appropriate materials specifically to meet the duty requirements. It also allows existing pumps to be adapted in service to meet changed duty conditions, merely by changing individual parts.

A general description of some of the more common materials used in Warman slurry pump construction is listed in table (2) below.

Table (2): Material specifications and descriptions

Step 10.                   PUMP SELECTION

Pump charts are provided by the manufacturer. Pump charts differ from one manufacturer to the next and between different types of pumps. Here, we will learn how to select a pump from the charts provided by the manufacturer.

SELECTION CHART FOR CENTRIFUGAL PUMPS

A selection chart as shown in Figure (e) makes it possible to do a preliminary pump selection by looking at a wide range of pump casing sizes for a specific impeller speed. This chart helps narrow down the choice of pumps that will satisfy the system requirements.

Figure (e): Pump family selection chart

For example, if the application called for a pump running at a nominal 1,800 revolutions per minute (rpm), that could provide 1,000 gallons per minute (gpm) at 100 feet of total head, the chart shows that 5 × 6 × 11 and 6 × 8 × 11 size pumps overlap on the selection chart and will likely be the two best sizes to evaluate further.

PERFORMANCE CURVE CHART

The following figure shows a typical pump performance chart for a given model, casing size, and impeller rotational speed. A great deal of information is crammed into one chart and this can be confusing at first.

Figure (f): Performance Curve Chart

Here, the Y axis (vertical) on this curve is the total dynamic head in feet and meters, and the X axis (horizontal) is the capacity (flow rate) in m3/hr and gpm.

Using the selection chart to narrow down the appropriate pump’s size for the duty point of 1,000 gpm and 100 feet of head, the manufacturer’s published curves can be referenced to help

determine the best pump for an application. Figure (f) shows the performance curve for a 5 × 6 × 11 pump running at 1,770 rpm. Information can be derived from the manufacturer’s pump curve for this application, including the following:

Note that data displayed on a manufacturer’s pump curve is based on 68 F or 20 C water. If a liquid other than water will be pumped, information on the manufacturer’s published curve must be adjusted for the liquid density and viscosity, which affects the head, flow, efficiency and pump input power.

It is necessary to understand the chart in detail.

#### Performance Curve

A performance curve, also called head capacity curve, is a plot of Total Head vs. flow rate for a specific impeller diameter and speed. It is represented by downward sloping blue line in the above figure. The plot starts at zero flow. The head at this point corresponds to the shut-off head of the pump. Starting at this point, the head decreases until it reaches its minimum. This point is sometimes called the run-out point and represents the maximum flow of the pump. Beyond this, the pump cannot operate.

Each number above the head capacity curves to the right of the Y axis represents different impeller diameters.

For a new pump, our calculations of Total Head for a given flow rate will help determine the impeller diameter to be selected according to the performance curve. At flow rate of 1,000 gallons per minute (gpm) and total dynamic head of 100, the impeller diameter that meets the duty point falls between 10 and 10.5 inches.

Quite often, the operating point is located between two curves on the performance chart. We can calculate the impeller size required by linear interpolation. For example, if the operating point falls between the 10 inch and 10.5 inch impeller curve (see Figure (g)), the following equation will give the correct size:

Where, DOP is the required impeller diameter.

∆HOP is the pump total head at the operating point;

∆H10 is the pump total head at the intersection of the 10 inch impeller curve and flow rate;

∆H10.5 is the pump total head at the intersection of the 10.5 inch impeller curve and the flow rate.

Figure (g): Example for calculation of impeller diameter by linear interpolation

#### Efficiency Curves

The B.E.P. (best efficiency point) is the point of highest efficiency of the pump. The numbers in the circles above the topmost head capacity curve are the pump efficiency, and the lines stemming from these circles are lines of constant efficiency. All points to the right or left of the B.E.P have a lower efficiency.

In the given example, at flow rate of 1,000 gallons per minute (gpm) and total dynamic head of 100 feet, the pump is 85 percent efficient at the rated point and 86 percent efficient at the best efficiency point (BEP).

In selecting a pump, one of the concerns is to optimize pumping efficiency. It is good practice to examine several performance charts at different speeds to see if one model satisfies the requirements more efficiently than another. Whenever possible the lowest pump speed should be selected, as this will save wear and tear on the rotating parts.

#### Horsepower Curves

The horsepower curves give the power required to operate the pump within a certain range. For example (see Figure (f)), all points on the performance curve to the left of the 10 hp curve will be attainable with a 10 hp motor. All points to the left of 15 hp curve and to the right of the 10 hp curve will be attainable with a 15 hp motor. The horsepower can be calculated with the Total Dynamic Head, flow and efficiency at the operating point.

In the given figure, it is represented by somewhat greenish lines that run through the head capacity curves. It signifies lines of constant pump input power.

In the given example, the shaft power will be between 25 horsepower (hp) and 30 hp at the rated point. To ensure a non-overloading condition at the end of the curve, a 40-hp motor may be required.

#### NPSH Requirement Curves

The NPSH required by a centrifugal pump, at any given point on the Head/Quantity (H/Q) curve, is the minimum net amount of energy, that the fluid must have at the entrance to the impeller, to avoid cavitation. The pump manufacturer specifies a minimum requirement on the NPSH in order for the pump to operate at its design capacity.

The minimum NPSH required to avoid cavitation is shown on pump performance curves as “NPSH required” indicated by the vertical dashed lines with a triangle at the base and contains a number and word “NPSH”. The dashed lines are constant lines of NPSH (in feet) that the system must supply for the pump to operate with a 3 percent head loss. NPSH margin above this value is required for the pump to operate at the published head

In the given example, the value of NPSH3 is between 9 and 10 feet at the duty point.

Step 11.                   CALCULATION OF POWER OF PUMP

The power required can now be calculated using formula:

Calculate and choose the next highest kilowatt motor frame size.

NOMENCLATURE

Cv        Concentration of solids in mixture, by volume (percent)

Cw        Concentration of solids in mixture, by weight (percent)

D         Inside diameter of pipe (m)

D50       Average particle size of solids in a given dry sample. This size is equal to the screen aperture which would retain exactly 50% by weight of the total sample (mm or µm)

ER       Efficiency Ratio

f           Darcy Friction Factor (dimensionless)

FL        Limiting Settling Velocity Factory (dimensionless)

g          Gravitational constant (9.81 m/s2)

Hm       Total Dynamic Head Developed by Pump when Pumping Mixture: Head of mixture (m)

Hw       Total Dynamic Head developed by pump when pumping water: Head of mixture (m)

k          Pipe Material internal roughness

Leq       Total Equivalent Length of Pipe

P          Power consumed at pump shaft (kW)

Q         Mixture flow rate (m3/sec)

S          Specific Gravity of Dry Solids

Sm        Specific Gravity of Mixture

v          Average Velocity of slurry (m/s)

vL         Limiting Settling Velocity of mixture (m/s)