Class 15Pumps and Compressors

Pumps- Provide energy to move a liquid from one location to another- Increase elevation, pressure, or velocity of a liquid- Centrifugal (or kinetic) and displacement pumps - common

H (pump head) = [∆(v2)/(2g)] + ∆z + [∆P/(ρLg)]

H in units of ft or mv is velocity of liquid in units of ft/s or m/sz is elevation in ft or mP is pressure of the liquid in appropriate unitsg is gravitational acceleration (32.2 ft/s2 or 9.81 m/s2)ρL is liquid density in appropriate units∆ signifies change of conditions (discharge – suction)

Centrifugal Pump

Centrifugal Pumps

Pros - Simple operation, low cost, low maintenance, uniform flow,quiet operation, can handle liquids with solids

Cons – Cannot be operated at high head pressures, difficulty handling highly viscous fluids, narrow maximum efficiencyoperating conditions

Head (pressure) is developed by the speed of the rotorCapacity range: 0.5 to 2 x 104 m3/hrDischarge Heads: 2 or 3 m to ~4900 m (equiv to ~48 MPa)

(Typical maximum head for a single stage is 500 ft;with multiple stages, heads as high as 3200 ft can beobtained)

Select Centrifugal Pumpso Operating Point isLocated on the Characteristicat the Point of MaximumEfficiency

Efficiency

Head

Brake hp

For a given Centrifugal Pump, the Characteristic Curve MovesUpward with Increasing Rate of Rotation, N (rpm)

The Characteristic Curve Moves Upward with IncreasingImpeller Diameter

Effect of ViscosityIncreasing viscosity for a fixed

capacity, Q, decreases the pumphead and the pump efficiency,

and increases the brake horsepower

(Viscosity effectscan be

substantial)

Positive Displacement Pumps

Pros – Higher efficiency, highly viscous fluids OK, high head pressureCons – Limited capacity range, no solids, lubricating fluid requiredHead (pressure) is developed by the speed of the rotorCapacity range: ~0.01 to 0.1 m3/sec (~ 100 times lower capacity range

than centrifugal pump)Discharge Heads: up to 70 MPa

(Reciprocating or Rotary)

Design Procedure for Pumps1) Given the application, specify the type of pump (typically centrifugal

or positive displacement)2) Calculate (by hand or with simulator) the shaft work required

for the process operation3) Check pump curves prior to final pump selection (operate at

point of highest efficiency)

Wo = shaft work (in kW) = [H q ρL]/1000where: H = total dynamic head (N-m/kg)

q = volumetric flow rte (m3/sec)ρL = liquid density (kg/m3)

Wo = shaft work (in kW) = [H q]/1000where: H = total dynamic head (Pa)

q = volumetric flow rte (m3/sec)

or

Power Input = Power Output / Efficiency

Peters, Timmerhaus, and West(“Plant Design and EconomicsFor Chemical Engineers”,McGraw-Hill, 2003)

Compression and Expansion of Fluids

Gas compressors (and blowers and fans) are designed toincrease the velocity and/or pressure of gases

Fan – increases kinetic energy of the gas with a compression ratio no more than 1.1 (110%of suction pressure)

Blower – increases pressure head more than velocity compression ratio < 2

Compressor – increases velocity head very little, hasa compression ratio > 2

Classifications

- avoid liquids entering or condensing in compressors- gases moved via centrifugal force, displacement,

or momentum- because gases are compressible, ∆T between suction

and discharge gas is significant even for moderatecompression ratios

- power inputs are large because of large molar volumesof gases

- usually well insulated so heat losses are negligiblecompared to their power reqt’s (adiabatic)

Compressors

- ∆T may limit compression ratio in a single stage- need for multiple stages is usually dictated by

impellor rotation-rate limitations (centrifugal)- Multiple stages allow compression ratios up to 30:1

Centrifugal Compressors

Positive Displacement Compressors

-Single stage compressors limited to about 400oF dischargetemperature (compression ratios ~ 2.5-6 per stage)

-To achieve high compression ratios, use multistage reciprocatingcompressors with interstage water cooling

Screw CompressorLobed Blower

Peters et al. 2003

Design Procedures for Compressors

Power Requirements(Assuming Adiabatic Operation)

Had (adiabatic head) = R’T1[(k/(k-1)] [(p2/p1)((k-1)/k) – 1]

Where: k = Cp/CvCp = specific heat at constant pressureCv = specific heat at constant volumeHad (N-m/kg)R’ = gas law constant in kJ/(kg-K)T1 = inlet gas temperature (K)p1 = inlet pressure (kPa)p2 = outlet pressure (kPa)

Adiabatic Power (single stage compression)

Pad = m Had

where: m = mass flow rate of gas (kg/s)Pad = power (kW)

or

Pad = 2.78 x 10-4 Q1 p1 [(k/(k-1)] [(p2/p1){(k-1)/k} – 1]where: Q1 = volumetric gas flow rate at inlet (m3/hr)

Adiabatic Discharge Temperature

T2 = T1 [(p2/p1) {(k-1)/k}]

Adiabatic Power (multi-stage compression)

Pad = 2.78 x 10-4 Nst Q1 p1 [(k/(k-1)] [(p2/p1){(k-1)/(kNst)} – 1]

where: Nst = number of stages involved in the compressionT1 = temperature of gas at compressor inlet (K)T2 = temperature of gas at compressor discharge (K)

T2 = T1 [(p2/p1) {(k-1)/kNst}]

-Assuming equal division of compression work between stages-Intercooling of gas between stages back to T1

Adiabatic Efficiency

Efficiency = ideal power req’d / power actually consumed

Centrifugal Compressor: 70-80% efficientReciprocating Compressor: 60-80% efficientRotary Compressor: 60-80% efficient