5.6 Pumps and compressors

Pump and Compressor Classification

Pumps and compressors both move fluids through chemical process systems, but they serve different purposes. Pumps handle liquids (which are essentially incompressible), while compressors handle gases (which change volume significantly under pressure). Choosing the right type for a given application depends on the required flow rate, pressure, and fluid properties.

Types of Pumps

Centrifugal pumps use a spinning impeller to fling fluid outward, converting rotational energy into velocity and then pressure. They're the workhorse of the chemical industry because they handle high flow rates at low to moderate pressures. Think water supply systems or cooling water loops.

Positive displacement pumps trap a fixed volume of fluid and physically push it into the discharge pipe. They're subdivided into:

• Reciprocating (piston, plunger, diaphragm): fluid is pushed by a back-and-forth motion
• Rotary (gear, lobe, screw): fluid is swept forward by rotating elements

These are best for high-pressure, low-flow situations like chemical metering or dosing, where you need precise volume control.

Special-purpose pumps (jet pumps, air-lift pumps, electromagnetic pumps) exist for niche applications like deep well pumping, handling solid-liquid slurries, or moving corrosive fluids where mechanical parts would degrade.

Types of Compressors

Positive displacement compressors trap a fixed volume of gas and shrink that volume to raise the pressure. They include:

• Reciprocating (piston): good for high pressures at relatively low flow rates (e.g., refrigeration cycles, compressed air systems)
• Rotary (screw, scroll, vane): smoother operation, often used for moderate pressures

Dynamic compressors use a rotating impeller or blades to accelerate the gas, then convert that kinetic energy into pressure in a diffuser section. They include:

• Centrifugal compressors: radial flow, common in large-scale industrial processes
• Axial compressors: flow moves parallel to the shaft, used in gas turbines and jet engines

Dynamic compressors excel at high flow rates with low to moderate pressure ratios.

Power Requirements for Pumps and Compressors

Pump Power and Efficiency

The power a pump needs depends on how much fluid it moves, how high it needs to push that fluid (pressure head), and how dense the fluid is. The relationship is:

$W_{\text{pump}} = \frac{Q \times \Delta P}{\eta_{\text{pump}}}$

where $Q$ is the volumetric flow rate, $\Delta P$ is the pressure rise across the pump, and $\eta_{\text{pump}}$ is the pump efficiency (expressed as a decimal). You can also write this in terms of head:

$W_{\text{pump}} = \frac{Q \times \rho \times g \times h}{\eta_{\text{pump}}}$

where $\rho$ is fluid density, $g$ is gravitational acceleration, and $h$ is the head developed.

Pump efficiency is the ratio of useful fluid power out to mechanical shaft power in:

$\eta_{\text{pump}} = \frac{\text{Fluid power output}}{\text{Shaft power input}} \times 100\%$

Efficiency is always less than 100% because of friction in bearings and seals, internal leakage, and turbulence losses. Typical centrifugal pump efficiencies range from about 60% to 85% depending on size and design.

Compressor Power and Efficiency

Compressor power calculations are more involved because gases change density as they're compressed. For an ideal (isentropic) compression, the work per unit mass is:

$W_{\text{isentropic}} = \frac{k}{k-1} \cdot R \cdot T_1 \left[\left(\frac{P_2}{P_1}\right)^{(k-1)/k} - 1\right]$

where $k$ is the specific heat ratio ($c_p / c_v$), $R$ is the specific gas constant, $T_1$ is the inlet temperature, and $P_2/P_1$ is the pressure ratio.

The actual power required is always higher than the isentropic value because real compression involves friction and heat transfer. Isentropic efficiency captures this:

$\eta_{\text{isentropic}} = \frac{W_{\text{isentropic}}}{W_{\text{actual}}} \times 100\%$

So the actual power input is:

$W_{\text{actual}} = \frac{\dot{m} \times W_{\text{isentropic}}}{\eta_{\text{isentropic}}}$

where $\dot{m}$ is the mass flow rate. Typical compressor isentropic efficiencies fall in the 70%–90% range.

Net Positive Suction Head (NPSH)

Definition and Importance

Net Positive Suction Head (NPSH) is the absolute pressure at the pump suction inlet, expressed as head of liquid, minus the vapor pressure of that liquid at the pumping temperature. It tells you how close the liquid at the pump inlet is to boiling. If the pressure drops too low, the liquid starts to vaporize inside the pump, which causes cavitation.

There are two values you need to compare:

• NPSHa (available): what the system provides to the pump inlet
• NPSHr (required): what the pump needs to operate without cavitation (specified by the manufacturer)

NPSH Available and Required

NPSHa depends on your piping layout and operating conditions. It's calculated as:

$\text{NPSHa} = \frac{P_{\text{surface}}}{\rho g} + h_s - h_f - \frac{P_{\text{vapor}}}{\rho g}$

where $P_{\text{surface}}$ is the pressure on the liquid surface in the suction vessel, $h_s$ is the static height of liquid above the pump centerline (negative if the pump is above the liquid), $h_f$ is the friction head loss in the suction piping, and $P_{\text{vapor}}$ is the vapor pressure of the liquid.

NPSHr is determined by the pump manufacturer through testing. It varies with flow rate and impeller speed.

The rule for safe operation: NPSHa must exceed NPSHr, typically by a margin of at least 0.5 to 1.0 meter to account for uncertainties.

Cavitation and Prevention

Cavitation happens when the local pressure inside the pump drops below the liquid's vapor pressure. Tiny vapor bubbles form, travel to higher-pressure regions, and then violently collapse. These collapses produce intense, localized shock waves that pit and erode the impeller surface, generate noise and vibration, and reduce pump head and efficiency.

To prevent cavitation:

1. Increase suction head by raising the liquid level in the supply tank or lowering the pump elevation
2. Reduce suction line friction losses by using shorter, larger-diameter piping with fewer fittings
3. Lower the liquid temperature (which reduces vapor pressure)
4. Select a pump with a lower NPSHr for your operating flow rate

Performance Characteristics of Pumps and Compressors

Pump Curves

A pump curve is a graph that shows how a pump performs across a range of flow rates at a fixed speed and impeller diameter. It typically plots three things on the same chart:

• Head vs. flow rate: As flow rate increases, the head (pressure) the pump can deliver decreases. This is the primary curve you use for system matching.
• Efficiency vs. flow rate: Efficiency rises to a peak called the best efficiency point (BEP), then drops off on either side. You want to operate as close to the BEP as possible.
• Power vs. flow rate: Power consumption generally increases with flow rate, though the exact shape depends on the pump type.

To select a pump, you overlay the system curve (which shows the head the system requires at each flow rate) on the pump curve. The intersection is the operating point. If that point falls near the BEP, you have a good match.

Compressor Maps

A compressor map is the equivalent performance chart for dynamic compressors. It plots pressure ratio (discharge pressure / suction pressure) on the vertical axis against corrected mass flow rate on the horizontal axis.

Key features on a compressor map:

• Constant speed lines: Each curve represents a different rotational speed. Higher speeds produce higher pressure ratios and flow rates.
• Efficiency contours: Closed loops (like contour lines on a topographic map) showing regions of equal efficiency. The highest efficiency sits near the center of the map.
• Surge line: The left boundary. Operating to the left of this line means the flow rate is too low for the pressure ratio, causing flow reversal and dangerous vibrations. This is the most critical limit to avoid.
• Choke line: The right boundary. Here the gas velocity reaches sonic conditions somewhere in the compressor, and no additional flow can pass through regardless of how much you open downstream.

Safe, efficient operation means staying between the surge and choke lines, ideally near the peak efficiency contours.