Equipment sizing basics: pumps, vessels and heat exchangers at the early stage

Early in a project you rarely need final equipment designs, but you do need sizes: to estimate cost, to plan the plot, and to spot long-lead items. Preliminary sizing turns the design case from the heat and material balance into duties, volumes and areas that are good enough for these decisions. Vendors and detailed design refine them later.

The methods below are standard textbook approaches. The typical values quoted are orders of magnitude for early work; your company standards and the references you use take precedence.

Start from the right case

• Use the design case, not just normal operation. Design flows usually include a margin above normal, often in the range of 10–20 %, set by the project’s design basis.
• Use consistent properties. Density, viscosity, heat capacity and vapour pressure should come from the same balance and property package as the stream data.
• Record every assumption. Efficiencies, hold-up times and heat transfer coefficients will be revisited; make them easy to find.

Pumps

For a centrifugal pump the key outputs are differential head, power and a first check on suction conditions.

Differential pressure is the discharge pressure minus the suction pressure. The discharge pressure must cover the destination pressure, the static height, line and equipment losses, and the pressure drop across any control valve.

H = ΔP / (ρ g)   ·   P_hydraulic = Q × ΔP   ·   P_shaft = P_hydraulic / η

Suction check. The net positive suction head available (NPSHa) must exceed what the pump requires (NPSHr) with a margin. NPSHa is the suction pressure above the liquid’s vapour pressure, expressed as head, plus static head, minus suction line losses. Hot liquids near their boiling point and long suction lines deserve early attention.

Worked example

Water at 20 m³/h with a differential pressure of 4 bar (ρ = 1000 kg/m³). Assume 60 % pump efficiency for a first estimate.

• Q = 20 / 3600 = 0.00556 m³/s
• Head: H = 400 000 / (1000 × 9.81) ≈ 40.8 m
• Hydraulic power: 0.00556 × 400 000 ≈ 2.2 kW
• Shaft power: 2.2 / 0.6 ≈ 3.7 kW
• With a typical motor allowance of about 15 %, about 4.3 kW is needed, so the next standard motor size, 5.5 kW, would be selected for the estimate.

Vessels and drums

Process drums are usually sized on two requirements: enough liquid volume for control and surge, and enough cross-section for vapour to disengage from the liquid.

Liquid hold-up. Volume between control levels is the liquid flow multiplied by a hold-up time, typically a few minutes depending on the service and what the drum feeds. Company standards usually define these times.

Vapour–liquid separation. The Souders–Brown relation gives the maximum allowable vapour velocity:

v_max = K √((ρ_L − ρ_V) / ρ_V)

K depends on vessel orientation and internals such as a mesh mist eliminator; values of roughly 0.05–0.1 m/s are common starting points. The vapour flow divided by v_max gives the minimum area for disengagement.

Worked example

A horizontal reflux drum receives 12 m³/h of liquid. With a 10-minute hold-up, the working volume is 12 × 10 / 60 = 2.0 m³. If the working liquid occupies about half the drum, the total volume is about 4.0 m³. With a length-to-diameter ratio of 3 and ignoring the heads:

• V = (π D² / 4) × 3D, so D = (4V / 3π)^1/3 ≈ 1.19 m
• Round to D = 1.2 m and L ≈ 3.6 m tangent to tangent

Then check that the vapour space above the liquid gives enough area for the vapour flow.

Heat exchangers

Start with the duty, then the area:

Q = ṁ c_p ΔT   ·   A = Q / (U × ΔT_LM × F)

ΔT_LM is the log mean temperature difference, and F corrects it for multi-pass arrangements; an F below about 0.8 usually means another configuration is needed. For phase change, use the latent heat instead of c_p ΔT.

U, the overall heat transfer coefficient, carries the most uncertainty at this stage. Design references give typical ranges by service. For shell-and-tube exchangers, published ranges are of the order of 800–1500 W/m²K for water to water and 250–750 W/m²K for organic solvents to water, while gases are far lower.

Worked example

Cool 10 000 kg/h of an organic liquid (c_p = 2.2 kJ/kg K) from 80 °C to 40 °C with cooling water heated from 30 °C to 40 °C, in counter-current flow. Assume U = 400 W/m²K.

• Duty: Q = (10 000 / 3600) × 2.2 × 40 ≈ 244 kW
• Terminal differences: 80 − 40 = 40 K and 40 − 30 = 10 K
• ΔT_LM = (40 − 10) / ln(40 / 10) ≈ 21.6 K
• Area: 244 000 / (400 × 21.6) ≈ 28 m², or about 31 m² with F = 0.9
• Cooling water: 244 / (4.18 × 10) ≈ 5.8 kg/s, about 21 t/h

A 10 K approach at the cold end is reasonable for cooling water service. A much smaller approach would push the area up sharply and is worth questioning.

Before you hand sizes on

• Every size traces back to a stream and case in the heat and material balance.
• Margins are applied once, not stacked at every step.
• Assumed efficiencies, hold-up times and U values are listed with their source.
• Sizes are rounded to sensible standard values, such as motor ratings and vessel diameters.
• Equipment that drives cost or layout is flagged for an early vendor check.

Sizing in the same project as the balance

Sizing goes wrong most often when the numbers it depends on change and nobody notices. In Black Owl, equipment sizing works from the equipment on the process flow diagram, in the same project as the material balance, and equipment drawing sheets can be generated from the equipment data. Request early access to try it on your process, or read what goes into a heat and material balance first.

Want to run these numbers now? Try the free pump power, heat exchanger area and drum sizing calculators, which use the same methods.