Centrifugal Pumps Emphasis on Pump Calculations

1 Overview of the Article

This article is aimed at presenting an overview of centrifugal pumps with emphasis on pump sizing calculation. A brief overview of other types of pumps is also discussed.

Centrifugal pumps will be described generally and their application. Guideline for selecting pump parts material will be briefly discussed referencing API 610.

The pumps described in this article are those used for oil and gas applications.

Figure 1: Liquid Hydrocarbon Pumps

2 Introduction

Pumps are key components of any liquid process or transfer system. The transfer of liquid is achieved by connecting piping, hoses to the inlet and outlet of the pump. Note not all pumps have inlet piping connections. Pumps such as lift station pumps, submersible pumps do not require inlet piping because they are submerged in the liquid. Pumps have various applications, including domestic use for water transfer, oil and gas facilities for crude oil treatment, water treatment and injection, condensate handling, chemical injection, lube oil circulation cooling medium, fire water system, HVAC system, sewage etc. Though there are different pumps, the selection process of any pump is the most critical part of the design of an efficient pumping system. Expert must handle the pump type selection; however, general guidelines can aid the effective selection of pump type.

A Pump is a device that transfers fluid or slurries from one place to the other by mechanical action. Pumps generate head, adds energy or head to a system, i.e. they are used to take liquid at an inlet Pressure P1 and raise the Pressure at the discharge to P2 (P2 > P1).

In some instances, a pump driver is mistakenly described as the pump; note the pump is not self-driven; the most common pump driver is the electric motor. Other drivers include mechanical or manual drivers, including chains and sprockets attached to pumps mostly used locally for fetching water from local wells. Combustion engines such as diesel combustion engines are also used as pump drivers.

The selection of the driver type is dependent on the application. Most firewater system designs have diesel-driven pumps and electric motor-driven pumps (Minimum one running the other(s) on standby). This configuration is used because during fire incidence, electricity might be cut off. The diesel-driven pump then serves as the main firewater pump if this scenario occurs.

Figure 2: Electric Motor Driven Pumps and a Diesel Engine Driven Pump

Figure 3: Fluid Transfer Schematic Using Pump

2.1 Definitions and General Terms Associated with Pumps

See below some key terms and definitions related to pumps and the properties of fluids.

2.1.1 Mass

Mass is the quantity of a matter. Mass is related to the density and volume of a liquid. Mass in the SI unit is expressed in kilograms.

2.1.2 Volume

Volume is the space occupied by a given mass of liquid. In SI unit expressed in cubic meters (m³)

2.1.3 Flow Rate

Flow rate is the quantity of liquid transferred per unit time by a pump. Generally, pumps are rated in terms of liquid transported per unit time, i.e. cubic meters per hour (m³/hr)

2.1.4 Density

Density is the mass per unit volume of a liquid mostly expressed in kilogram per cubic meters (Kg/m³)

2.1.5 Specific Gravity

Specific Gravity is the ratio of the liquid density to the density of water at the same temperature. SG has no unit because the density of the liquid and water are expressed in the same unit.

2.1.6 Viscosity

The term viscosity is used to describe the resistance of a fluid to flow. It is a measure of the sliding friction between successive layers of liquid flowing through a pipeline

2.1.7 Pressure

The force acting per unit area at a certain point within the liquid is the pressure at that point. The pressure of a static fluid at a given point is referred to as hydrostatic pressure.

2.1.8 Vapour Pressure

Vapour pressure is the pressure at a given temperature at which liquid and vapour exist in equilibrium. The normal boiling point of a liquid is the temperature at which vapour pressure is equal to atmospheric pressure.

3 Classification of Pumps

There are two categories of pumps; Dynamic pumps and positive displacement pumps. The selection of any pump depends on the properties of the fluid, such as viscosity, temperature, density, sensitivity and chemical composition.

The pump application such as transfer, mixing, dosing, suction pressure, discharge pressure should also be considered.

3.1 Positive Displacement Pumps

Positive displacement pumps are not as prominent as dynamic pumps. They transfer fluid by trapping a fixed amount of fluid and force or displace the trapped fluid into the discharge piping. Positive displacement pumps can be classified into reciprocating, rotary or linear pumps based on the principle of operation. There are different types of reciprocating and rotary pumps, including the following

• Reciprocating pumps
  • Piston Pumps
  • Plunger pumps
  • Diaphragm pumps
• Rotary Pumps
  • Rotary Lobe pumps
  • Rotary Gear Pumps
  • Rotary Vane pumps
  • Screw Pumps

Figure 4: Cross Section of a Positive Displacement Pump

3.2 Dynamic Pumps

Dynamic or Rotodynamic pumps impart energy continuously to the fluid being pumped through an impeller or rotor. The most common types of Rotodynamic pumps are mixed flow, axial flow and centrifugal pumps. The centrifugal pump is the most prominent of all the Rotodynamic pumps. They have a wide range of applications in the oil and gas industry as well as utility applications.

4 CENTRIFUGAL PUMPS

A centrifugal pump is a mechanical device designed to transfer fluid utilizing rotational energy imparted on the impeller or rotors by a driver. The driver could be a motor, fuel combustion engine etc.  The fluid enters the rotating impeller along the pump axis (eye of the impeller). It is cast out through the impeller’s vane tips by centrifugal force along its circumference (tangentially or radially).  The impeller rotational action increases the fluid pressure and velocity and directs it towards the pumps discharge nozzle or outlet.  The impeller is installed inside the leak-tight casing.

Though centrifugal pumps are more prominent than positive displacement pumps, they tend to have a lower efficiency than positive displacement pumps; however, Centrifugal pumps deliver a higher flow rate in relation to the pump’s physical size.

The different types of centrifugal pumps are vertical centrifugal pumps, horizontal centrifugal pumps. Technically centrifugal pumps are classified as overhung (OH) pumps, Between Bearing (BB) Pumps, and vertically suspended (VS) pumps. Refer to API 610 (Centrifugal Pumps for Petroleum, Petrochemical and Natural Gas Industries) for more details.

4.1 Limitations of Centrifugal Pumps

As previously stated, experts should select pumps; however, there are limitations to selecting centrifugal pumps when the following scenarios are encountered.

• Centrifugal pumps are not recommended for pumping high viscous fluids; pumping viscous products would require an oversized pump that would deliver a flowrate outside the pump’s optimum specifications, resulting in higher power consumption. This means the efficiency of centrifugal pumps reduces with increasing fluid viscosity.
• If a particular quantity of fluid is required, such as dosing application, centrifugal pumps are not suitable for these applications. The positive displacement pumps suit this purpose. To use a centrifugal pump for doing the designer must use a flow meter to control the pump speed with the possibility of the pump operating outside of its optimum specification.
• Centrifugal pumps are generally not recommended for pumping sensitive liquid such as milk, wine, volatile liquid etc.

4.2 Centrifugal Pump Materials

The selection of materials for centrifugal pumps is not quite straightforward; the selection is based on the process parameters (temperature and pressure) and the fluid been transferred.

ANSI/API STANDARD 610 has provided a guide for the selection of pumps parts materials for centrifugal pumps. Note that the pumps covered by this standard are those used for petroleum, petrochemical, and natural gas industries.

Annexe G Table G.1 of API 610 shows the material selection guide. Also shown in Appendix H, table H.1 is details of Material classes for pump parts.

See below random extract from API 610. For complete take refer to Annex G, Table G.1

Table 1: Material Class Selection Guidance

Utilising the Annex G and H, pump parts materials such as pressure casing, impellers, shaft etc can be selected for various fluid applications. For more details consult the pump manufacturer.

5 Centrifugal Pumps Calculations

In addition to the previous definitions, the following definitions are key in pump calculations

5.1 Head

This is the depth in feet or meters corresponding to the pressure exerted by the liquid flowing through a pipe. In pump sizing, there are different heads, as stated below.

5.1.1 Pressure Head

This is the corresponding height of the liquid to the pressure. The corresponding head to water-filled vessel at 200KPa is estimated below

Pressure (P) = 200KPa

Density of Water = 1000Kg/m³

Acceleration due to gravity g = 10m/s2

h = Pressure Head

This implies that the corresponding head is

Assuming a vessel is filled water and the pressure in the vessel is200 KPa, the corresponding pressure head is 20m height of water

5.1.2 Velocity Head

This is the head generated as a result of the movement of the liquid. This is usually small compared to the pressure head.

5.2 Reynolds Number

This is a dimensionless parameter used in classifying the fluid flow in pipes. The Reynold’s number (R) is calculated using the formula below

Be mindful of the units, formula will change with various multiplying factors when working with other units.

5.3 Laminar Flow

Laminar flow, also known as viscous or streamline flow, is a flow in which the fluid flow in layers without causing eddies or turbulence. If the fluid flows through a transparent pipe and we inject a dye into the flowing stream, the dye will show a smooth straight line in the stream, confirming laminar flow. For laminar flow, the calculated Reynold’s number (R) is lesser than 2000 (R < 2000)

5.4 Turbulent Flow

Turbulent flow is characterized by the formation of eddies or turbulence. The calculated Reynold’s number for turbulent flow is greater than 4000 (R > 4000)

5.5 Critical Flow

This type of flow is neither laminar nor turbulent. The calculated Reynold’s number is between 2000 and 4000 (R > 2000 and R < 4000).

5.6 Losses

As the fluid flows through the piping, there is a loss of energy resulting from the interaction between the internal pipe surface and the liquid molecules (friction losses) and the flow-through fitting such as elbows, tees, etc. and valves (minor losses). This loss results in a pressure drop at the suction side of the pump and the discharge side of the pump. The pressure drop due to friction depends on fluid flow rate, viscosity and the liquid specific gravity. All the losses (Friction loss and minor loss) must be factored into the pump calculations, including the appropriate length of pipe, the number of valves and fittings.

Several formulas have been developed to predict the minor losses across valves and fitting; however, another efficient way of doing this is by converting these losses to equivalent pipe length. In SPDC DEP 31.38.01.11-Gen, each fitting has been assigned an equivalent length of pipe; therefore, it is easier to estimate the minor loss using this method. The below table shows the equivalent length for fittings and valves as extracted from Table 6. DEP 31.38.01.11-Gen.

Table 2: Pipe Equivalent Length for Fittings and Valves

Where

D = Nominal Pipe Diameter

For reducing fittings D = large end nominal diameter and d = small end nominal diameter.

In critical situations, the Manufacturer/Supplier’s data shall be obtained.

The pressure drop due to friction in any given length of pipe, expressed in liquid head (h), can be calculated using the Darcy-Weisbach developed equation.

In terms of pressure this can be re-written as

Where

f = Darcy friction factor dimensionless

L = Length of Pipe

D = Pipe Internal Diameter

DP = Pressure Drop

H = Head Loss

V= Average Liquid Flow Velocity

p = Density of the Liquid

In laminar flow, the friction factor depends only on Reynold’s number, while in turbulent flow, it depends on the pipe diameter, internal pipe roughness, and Reynold’s number.

For Laminar Flow

For Turbulent Flow

There are various formula that are applicable, however the most popular and applicable is the Colebrook-White equation

The friction factor (f) is calculated iteratively (trial and error)

5.7 Net Positive Suction Head

The total suction absolute head, at the suction nozzle, referred to the standard datum, minus the liquid vapor absolute pressure head, at the operating temperature. It is in two parts the Net Positive Suction Head Available (NPSH_A) and Net Positive Suction Head Required (NPSH_R)

Mathematically

Where

h_p = pressure head

h_vpa = vapor pressure head

h_st = liquid static head

h_f = friction losses head

h_v = velocity head

The NPSH available (NPSH_A) is a network characteristic independent of the pump, which the purchaser must define to correctly select a pump.

For every pump, there is a minimum NPSH below which cavitation will occur, this is known as the NPSH required (NPSH_r)

Every pump manufacturer determines the NPSH required of its pumps by forced cavitation tests.

NPSH_A must be greater than NPSH_R by a determined value for the pump to operate efficiently without cavitation. In most cases, a value of 1m to 2m, except when the liquid contains dissolved gasses, may be used a value of 5m. Note the pump manufacturer shall determine the actual margin.

6 References

ANSI/API Standard 610: Petrochemical and Natural Gas Industries Petrochemical and Natural Gas Industries

DEP 31.29.02.30-Gen: Centrifugal Pumps (Amendments/Supplements to ISO 13709)