Process Design of Pump

Table of Contents

Before moving to the Process Design of the Pump, let’s understand some basic things about pumps

“A pump is a device used in the flow system of liquid to increase the mechanical energy of the flowing liquid.”

Pumps are classified mainly into two categories
1. Dynamic Pumps (eg. Centrifugal Pump)
2. Positive Displacement Pumps (eg. Reciprocating Pump, Rotary Pump)

Important Terminologies

Some of the important terminologies used with the pumps are as follows.

Capacity of Pump $(q_v)$
Total Dynamic Head
1. Total Discharge Head $(h_d)$
2. Total Suction Head $(h_s)$
Net Positive Suction Head (NPSH)

Capacity of Pump $(q_v)$

”Flow rate $(q_v)$ of fluid created by the pump is known as capacity of the pump.”

In SI units, capacity is expressed in m³/h or L/s.

Total Dynamic Head $(H)$

The total dynamic head $(H)$ of a pump is the difference between the total discharge head $(h_d)$ and total suction head $(h_s)$ .

$H=h_d-h_s$

Where,
H =Total dynamic head, measured in Liquid Column (LC) unit.
$h_d$ =Total Discharge Head, measured in Liquid Column (LC)
$h_s$ =Total Suction Head, measured in Liquid Column (LC)

Total Discharge Head $(hd )$

The total Discharge Head (hd ) of the pump can be measured in two conditions, before installation of the pump or after installation of the pump.

Before Installation of the Pump

$h_d = h_{sd} + h_{fd}$

Where,
$h_{sd}$ = Static Discharge Head
$h_{fd}$ = Frictional Loss in Discharge Line

Static Discharge Head (hsd ) can be calculated using the following equation.

$h_{sd} = p' \pm z'$

Where,
p′ = Absolute pressure over the free surface of the liquid in the receiver
Z′ = Vertical distance between the free surface of the liquid in the receiver and the centerline of the pump placed horizontally (For a vertical pump Z′ is the distance between the free surface of the liquid and the eye of the suction of the impeller).

If the pump is below the level of the free surface of the liquid in the receiver.

$h_{sd} = p' + z'$

If the pump is placed above the free surface of the liquid in the receiver.

$h_{sd} = p' - z'$

After the Installation of the Pump or During Operation

$h_d=h_{gd}+atm\; Pressure + h_{vd}$

Where,
hgd= Discharge gauge pressure measured by the pressure gauge. If pressure is below atmospheric, a vacuum gauge reading is used for hgd in the above equation but with a negative sign.
hvd = Velocity head at the point of gauge attachment in the discharge line

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Total Suction Head (hs)

Total Suction Head $(h_s)$ of the pump can also be measured in two conditions, before installation of the pump or after installation of the pump.

Before Installation of the Pump

$h_s = h_{ss} + h_{fs}$

Where,
$h_{ss}$ = Static Suction Head
$h_{fs}$ = Frictional Loss in Suction Line

Static Suction Head $(h_{ss})$ can be calculated using the following equation.

$h_{ss} = p \pm z$

Where,
$p$ = Absolute pressure over the free surface of the liquid in the source
$Z$ = Vertical distance between the free surface of the liquid at the source and the centerline of the pump placed horizontally (For vertical pump Z is the distance between the free surface of liquid and the eye of suction of impeller).

If the pump is going to be installed below the free surface of the liquid

$h_{ss} = p + z$

If the pump is going to be installed above the free surface of the liquid

$h_{ss} = p - z$

After the Installation of the Pump or During Operation

$h_s=h_{gs}+atm\; Pressure + h_{vs}$

Where,
$h_{gs}$ = Suction gauge pressure
$h_{vs}$ = Velocity head at the point of gauge attachment

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Net Positive Suction Head (NPSH)

The net positive suction head is the total head (velocity head + pressure head) in the suction line minus vapor pressure head of the liquid.

When pump installation is designed,

$(NPSH)_A \geq (NPSH)_R$

$(NPSH)_A$ = Net Positive Suction Head Available

$(NPSH)_R$ = Net Positive Suction Head Required

$(NPSH)_R$ is normally specified by the pump supplier

$(NPSH)_A$ should be calculated and specified by the process engineer.

When $(NPSH)_A$ is less than $(NPSH)_R$ , cavitation can take place, and bubbles of vapor form in the suction line.

Eventually, these bubbles collapse inside the casing of the pump when pressure is exerted on them by the impeller of the pump.

Such collapse of bubbles can cause severe erosion and damage to the pump.

It may form minor cavities on the inside surface of the casing and of the impeller. Hence, this phenomenon is called cavitation.

Theoretically, $(NPSH)_A$ should be greater than zero to avoid cavitation.

$(NPSH)_R$ depends on the properties of the liquid, the total liquid head, pump speed, capacity, and impeller design.

Practical curves of $(NPSH)_R$ vs capacity and speed of pump are supplied by the pump manufacturer.

$(NPSH)_A$ Calculation

Before Installation of the Pump

$(NPSH)_A =h_{ss}-h_{fs}-p_v$

Where,
$h_{ss}$ = Static suction head, m LC = p ± Z
$h_{fs}$ = Friction loss in the suction line, m of liquid column (LC)
$p_v$ = Vapour pressure of liquid at suction temperature expressed in m of liquid column (LC)

For existing installation

$(NPSH)_A = atm \; pressure + h_{gs} - p_v + h_{vs}$

Where,
$h_{gs}$ = Suction gauge pressure, m of liquid column (LC)
$p_v$ = Vapour pressure of liquid at suction temperature expressed in m of liquid column (LC)
$h_{vs}$ = Velocity head at the point of gauge attachment, m of liquid column (LC)

As a general guide $(NPSH)_A$ should preferably be above $3 \; m$ for pump capacities up to a flow rate of $100\; m^3/h$ , and $6 \;m$ above this capacity.

For a given system, if $(NPSH)_A$ is less than $(NPSH)_R$ , following remedial measures are recommended:

Change the location of the pump to improve $(NPSH)_A$ . In other words, positive suction head $(h{ss})$ may be increased.
Provide jacketed cooling in the suction line to decrease the vapor pressure $(p_v)$ of the liquid.
Reduce the operating speed of the pump; thereby specific speed of the pump is reduced and its $(NPSH)_R$ is less.

NPSH Requirement for Liquids Saturated with Dissolved Gases

In many situations, the liquid to be pumped is saturated with gases, which have definite solubilities in the liquid. When a suction system for such a liquid is to be designed for a centrifugal pump, $(NPSH)_A$ calculations are different.

For Example, Pumping of cooling water (saturated with air), pumping of condensate from a knock-out drum of a compressor, pumping of solution from an absorber, etc.,

Dissolved gases start desorbing when the pump is started and suction is generated at the pump eyes.

Normally, a pump can tolerate 2 to 3% flashed gases at the pump eye without encountering cavitation.

If the design of the suction system is made to restrict about 2.5 % flash, it is considered safe for the pump operation.

For a liquid saturated with dissolved gases, $p_v$ is replaced by $p_{va}$ which is called artificial liquid vapor pressure. For evaluation of $p_{va}$ , following procedure is recommended:

Calculate the molar mass of the gas mixture, dissolved in the liquid.
Calculate mass fraction $(w_o)$ of the dissolved gas mixture.
Calculate pseudo-critical properties of the dissolved gas mixture, if system pressure is high.
Calculate the specific volume of the dissolved gas mixture $(V_{Ga})$ at the operating conditions.

Steps (1) to (4) can be avoided if the solubility of the gas mixture in the liquid (such as air in water) is known from the literature.

Calculate the volume fraction of the dissolved gas $(GVP)$ in a hypotheoretical gas-liquid mixture.

Consider one unit mass of the liquid in which the gas mixture is dissolved.
If GVP is less than or equal to 2.5%, $(NPSH)_A$ can be safely used to calculate $(NPSH)_A$ using vapor pressure $(p_v)$ of the liquid at the operating temperature.
If higher than calculate volume fraction (a) of the flashed gas mixture (as pressure is lowered) over the liquid, saturated with the dissolved gas mixture, using the following equation.

$a=\left[\frac{1}{\frac{\left(\frac{p}{p_0}-\frac{p_v}{p_0}\right)^2\left(1-\frac{p_v}{p_0}\right)}{\left(\frac{V_{Ga}}{V_L}\right)\left(\frac{p}{p_0})(1-\frac{p}{p_0}\right)}+1}\right]$

This equation assumes that the dissolved gas mixture follows the ideal gas law, Dalton’s law, and Henry’s law.

Where,
$p$ = liquid pressure at pump eye, $kPa$
$p_v$ = vapour pressure of liquid at the operating temperature, $kPa$
$p_0$ = system pressure, $kPa$
$V_{Ga}$ = specific volume of the dissolved gas mixture, $m^3/kg$
$V_L$ = specific volume of the liquid at the operating conditions, $m^3/kg$

Calculate a for different values of p. Draw a graph of $a$ vs $p$ . Read p corresponding to a = 0.025 which is called $p_{va}$ . Alternately by trial and error, calculate $p_{va}$ , for a = 0.025.

Use $(NPSH)_A$ and insert $p_{va}$ in place of $p_v$ and calculate $(NPSH)_A$ .

Power Required for Pumping

The power required for pumping an incompressible fluid is given by the equation:

$P=\frac{H \; q_v \; \rho}{3.67 \times 10^5 \times \eta }$

Where,
$P$ = Power Required, $kW$
$H$ = Total Dynamic Head, m of liquid column (LC)
$q_v$ = Capacity, $m^3/h$
$\rho$ = Fluid Density, $kg/m^3$
$\eta$ = Efficiency of Pump

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Standard Pipe Size Chart