Formula sheet

Chemical Process Heat Transfer and Utility Systems Formula Sheet

Chemical process heat-transfer formulas for heat duty, LMTD, exchanger area, fouling, cooling water, steam, heat recovery, pumping power, and utility capacity.

Branch: Chemical Engineering
Content: Formula sheet
Updated: Jul 03, 2026
Revision: v1.1.0 · reviewed

This formula sheet collects first-pass calculations for chemical process heat-transfer and plant utility systems. Use it to screen exchanger duty, cooling-water demand, steam consumption, fouling impact, heat recovery, pumping power, and utility header capacity before detailed equipment design or plant troubleshooting.

These equations support engineering judgement; they do not replace verified physical properties, exchanger geometry, pressure-drop calculations, relief review, materials compatibility, control validation, or site utility standards. State the process boundary, sign convention, operating case, cleanliness condition, and property basis before using the results.

How to Use This Formula Sheet

Use this sheet to connect process heat duty, exchanger performance, utility loads, steam and condensate behavior, cooling-water demand, fouling, pumping power, heat recovery, and control or safety margins. Start by defining the process boundary, stream names, phase state, operating case, sign convention, property package, cleanliness condition, utility header, control strategy, and acceptance criterion. Then decide whether the calculation supports design screening, troubleshooting, debottlenecking, startup review, utility capacity planning, or performance testing.

Work through the formulas in this order:

Establish heat duty and hot/cold-side energy balance before using LMTD, NTU, fouling, or utility sizing.
Check physical properties, phase change, pressure, temperature, flow, fouling state, and exchanger arrangement before comparing area or $U$ values.
Check cooling water, chilled water, steam, condensate, heat recovery, pump power, utility diversity, controls, and safety margins under separate normal, fouled, startup, turndown, hot-weather, and abnormal cases.
Compare calculations with measured flow, temperatures, pressure drop, steam rate, condensate return, utility header pressure, fouling trend, and product-quality evidence.
Convert the result into an action: accept, clean, retube, rebalance utility flow, adjust controls, change startup sequence, add capacity, or escalate safety review.

Do not diagnose fouling or utility shortfall from one side of the exchanger alone. Heat-balance closure, pressure-drop trend, instrument health, property assumptions, phase behavior, and control position should be checked together.

Basis and Validity Limits

The formulas below are first-pass screens. They assume that stream properties, phase state, flow arrangement, fouling state, pressure drop, measurement basis, and operating case are known.

LMTD, NTU, and $U$ calculations are valid only when the exchanger arrangement, terminal temperatures, correction factor, heat-transfer area, fouling resistance, and phase behavior match the service. Multipass, boiling, condensation, maldistribution, bypassing, noncondensables, and viscosity changes can invalidate a simple clean-duty estimate.

Utility formulas are valid only when header pressure, return temperature, diversity, seasonal condition, control-valve authority, condensate drainage, water treatment, pump curve, cavitation margin, and simultaneous demand are considered. Nominal capacity can fail during startup, cleaning, regeneration, or partial outage.

Control and safety estimates are screening checks. Loss of cooling, excess heating, blocked-in liquid expansion, water hammer, relief loading, runaway cooling demand, fouling-driven temperature drift, and interlock response require process-safety and controls review beyond steady-state heat duty.

Notation and Unit Basis

Common symbols:

Symbol	Meaning	Typical units
$\dot{Q}$	heat-transfer rate or heat duty	kW, MW
$\dot{m}$	mass flow rate	kg/s
$Q_v$	volumetric flow rate	m^3/s
$C_p$	specific heat capacity	kJ/(kg K)
$C$	heat-capacity rate, $\dot{m}C_p$	kW/K
$U$	overall heat-transfer coefficient	W/(m^2 K)
$A$	heat-transfer area	m^2
$F$	LMTD correction factor	dimensionless
$\Delta T_{lm}$	log-mean temperature difference	K
$R_f$	fouling resistance	m^2 K/W
$\eta$	efficiency	dimensionless

Use temperature differences in kelvin or degrees Celsius consistently. A temperature difference of $1\ \text{K}$ is numerically equal to $1^\circ\text{C}$ .

Heat Duty

Sensible heat duty for one stream:

\dot{Q}=\dot{m}C_p(T_{out}-T_{in})

Heat duty from volumetric flow:

\dot{Q}=\rho Q_v C_p(T_{out}-T_{in})

Phase-change duty:

\dot{Q}=\dot{m}\Delta h_{phase}

Approximate reaction heat load:

\dot{Q}_{rxn}\approx -\Delta H_{rxn}\dot{\xi}

where $\dot{\xi}$ is reaction extent rate. Check the sign convention. In plant utility calculations it is often clearer to use heat removed or heat added as a positive magnitude and state the service explicitly.

Heat flux:

\displaystyle q''=\frac{\dot{Q}}{A}

Heat flux is useful for checking boiling, fouling, wall temperature, thermal degradation, and localized overheating. It should not be interpreted without surface geometry and fluid-side conditions.

Heat-Exchanger Energy Balance

For a two-stream exchanger with negligible external heat loss:

\dot{Q}_{hot}+\dot{Q}_{cold}=0

Using positive magnitudes:

\dot{Q}=\dot{m}_h C_{p,h}(T_{h,in}-T_{h,out})

\dot{Q}=\dot{m}_c C_{p,c}(T_{c,out}-T_{c,in})

Heat-balance closure error:

\displaystyle e_Q=\frac{\left|\dot{Q}_{hot}-\dot{Q}_{cold}\right|}{\max(\dot{Q}_{hot},\dot{Q}_{cold})}

Small mismatch can come from heat loss, instrument uncertainty, property error, or non-steady operation. Large mismatch should be resolved before diagnosing fouling or resizing equipment.

LMTD Method

Overall exchanger relation:

\dot{Q}=UA F\Delta T_{lm}

Area from required duty:

\displaystyle A=\frac{\dot{Q}}{UF\Delta T_{lm}}

Log-mean temperature difference:

\displaystyle \Delta T_{lm}=\frac{\Delta T_1-\Delta T_2}{\ln(\Delta T_1/\Delta T_2)}

For counterflow exchangers:

\Delta T_1=T_{h,in}-T_{c,out}

\Delta T_2=T_{h,out}-T_{c,in}

If $\Delta T_1$ and $\Delta T_2$ are nearly equal, $\Delta T_{lm}$ approaches the common temperature difference. For multipass shell-and-tube, crossflow, or strongly nonideal arrangements, use the correction factor $F$ from the appropriate exchanger method. Values of $F$ near or below about 0.75 often indicate a poor temperature program or unsuitable arrangement.

Overall Coefficient and Fouling

Simplified flat-wall resistance model:

\displaystyle \frac{1}{U}=R_i+R_{wall}+R_o+R_{f,i}+R_{f,o}

For convection terms:

\displaystyle R_i\approx \frac{1}{h_i}

\displaystyle R_o\approx \frac{1}{h_o}

Apparent fouling resistance from measured clean and dirty coefficients:

\displaystyle R_{f,app}=\frac{1}{U_{dirty}}-\frac{1}{U_{clean}}

Duty ratio at unchanged area and temperature program:

\displaystyle \frac{\dot{Q}_{dirty}}{\dot{Q}_{clean}}\approx\frac{U_{dirty}}{U_{clean}}

This ratio is only approximate because fouling can also change flow, pressure drop, phase behavior, and terminal temperatures. In troubleshooting, confirm duty loss with both hot-side and cold-side heat balances.

Effectiveness-NTU Checks

Heat-capacity rate:

C=\dot{m}C_p

Minimum and maximum heat-capacity rates:

C_{min}=\min(C_h,C_c)

C_{max}=\max(C_h,C_c)

Capacity-rate ratio:

\displaystyle C_r=\frac{C_{min}}{C_{max}}

Maximum possible heat transfer:

\dot{Q}_{max}=C_{min}(T_{h,in}-T_{c,in})

Effectiveness:

\displaystyle \epsilon=\frac{\dot{Q}}{\dot{Q}_{max}}

Number of transfer units:

\displaystyle NTU=\frac{UA}{C_{min}}

The relation between $\epsilon$ , $NTU$ , and $C_r$ depends on flow arrangement. Use the correct relation for counterflow, parallel flow, shell-and-tube, crossflow, or phase-change service. This method is helpful when outlet temperatures are unknown.

Cooling-Water and Chilled-Water Demand

Cooling-water mass flow:

\displaystyle \dot{m}_{cw}=\frac{\dot{Q}}{C_{p,w}(T_{return}-T_{supply})}

Approximate cooling-water volumetric flow:

\displaystyle Q_{v,cw}=\frac{\dot{m}_{cw}}{\rho_w}

Cooling tower or heat-rejection load:

\dot{Q}_{reject}\approx \dot{Q}_{process}+\dot{W}_{pump}+\dot{W}_{compressor}

For chilled water, refrigeration, or glycol systems, use the actual fluid properties at operating concentration and temperature. For refrigeration, a lower evaporating temperature usually increases compressor power and reduces coefficient of performance.

Steam, Condensate, and Reboiler Duty

Steam mass flow from useful latent heat:

\displaystyle \dot{m}_{steam}=\frac{\dot{Q}}{\Delta h_{vap,useful}}

If condensate leaves subcooled or if superheat is desuperheated before condensation, include sensible terms:

\dot{Q}=\dot{m}_{steam}(h_{steam,in}-h_{condensate,out})

Approximate reboiler vapor generation:

\displaystyle \dot{m}_{vapor}\approx \frac{\dot{Q}_{reb}}{\Delta h_{vap,process}}

Steam load with distribution loss allowance:

\dot{m}_{steam,total}=\dot{m}_{steam}(1+f_{loss})

Condensate return energy recovered:

\dot{Q}_{cond,return}=\dot{m}_{cond}C_{p,w}(T_{cond}-T_{makeup})

Steam calculations must be checked against steam pressure, saturation temperature, control-valve authority, condensate drainage, water hammer risk, trap capacity, noncondensable venting, and exchanger pressure rating.

Heat Recovery and Utility Savings

Recovered heat duty:

\dot{Q}_{rec}=\min(\dot{Q}_{hot,available},\dot{Q}_{cold,demand})

Annual recovered energy:

E_{rec}=\dot{Q}_{rec}t_{op}

Fuel energy avoided:

\displaystyle E_{fuel,avoided}=\frac{E_{rec}}{\eta_{boiler}}

Cooling load avoided:

\dot{Q}_{cooling,avoided}\approx \dot{Q}_{rec}

Simple annual value:

V_{annual}=E_{fuel,avoided}c_{fuel}+E_{cooling,avoided}c_{cooling}

Heat recovery is limited by temperature level, schedule matching, fouling, corrosion, contamination consequence, pressure drop, startup operability, and bypass control. A heat-recovery exchanger can save energy while reducing reliability if those constraints are ignored.

Hydraulic and Pumping Power Checks

Mass flow from volumetric flow:

\dot{m}=\rho Q_v

Average velocity:

\displaystyle v=\frac{Q_v}{A_{flow}}

Reynolds number:

\displaystyle Re=\frac{\rho vD}{\mu}

Pump hydraulic power:

\dot{W}_{hyd}=\Delta p Q_v

Pump shaft power:

\displaystyle \dot{W}_{shaft}=\frac{\Delta p Q_v}{\eta_{pump}}

Pressure-drop increase from fouling or restriction:

\Delta p_{increase}=\Delta p_{measured}-\Delta p_{clean}

Higher velocity may improve heat transfer but can raise pumping power, erosion, vibration, valve pressure drop, water hammer severity, and cavitation risk. Thermal and hydraulic calculations should be reviewed together.

Utility Header Capacity and Diversity

Total connected utility load:

\dot{Q}_{connected}=\sum_i \dot{Q}_{i,max}

Coincident peak load:

\dot{Q}_{peak}=\sum_i f_i\dot{Q}_{i,max}

where $f_i$ is a coincidence or diversity factor for service $i$ .

Utilization ratio:

\displaystyle u=\frac{\dot{Q}_{peak}}{\dot{Q}_{available}}

Remaining margin:

M_Q=\dot{Q}_{available}-\dot{Q}_{peak}

Percent margin:

\displaystyle M_{\%}=\frac{\dot{Q}_{available}-\dot{Q}_{peak}}{\dot{Q}_{available}}(100)

Capacity should be checked for normal production, startup, cleaning, regeneration, hot weather, low steam pressure, partial equipment outage, emergency cooling, and future debottlenecking. Header pressure and temperature can fail before nominal heat duty is fully consumed.

Control and Safety Margins

Controller duty margin:

M_{control}=\dot{Q}_{max,available}-\dot{Q}_{required}

Valve turndown ratio:

\displaystyle TR=\frac{Q_{v,max}}{Q_{v,min,controllable}}

Thermal time constant estimate:

\displaystyle \tau\approx \frac{m C_p}{UA}

Approximate temperature ramp for a well-mixed inventory:

\displaystyle \frac{dT}{dt}\approx \frac{\dot{Q}_{in}-\dot{Q}_{out}+\dot{Q}_{rxn}}{mC_p}

These estimates help review startup ramps, runaway cooling demand, loss-of-utility scenarios, integral windup, alarm response time, and interlock setpoints. A heat-transfer calculation is incomplete if it only proves normal steady-state duty.

Worked Example 1: Cooling-Water Flow for a Product Cooler

A product cooler must remove $\dot{Q}=2.40\ \text{MW}$ . Cooling water enters at $28^\circ\text{C}$ and is allowed to leave at $38^\circ\text{C}$ . Use $C_{p,w}=4.18\ \text{kJ/(kg K)}$ and $\rho_w=1000\ \text{kg/m}^3$ .

Cooling-water mass flow:

\displaystyle \dot{m}_{cw}=\frac{2400}{4.18(38-28)}=57.4\ \text{kg/s}

Volumetric flow:

\displaystyle Q_{v,cw}=\frac{57.4}{1000}=0.0574\ \text{m}^3/\text{s}

Convert to cubic meters per hour:

Q_{v,cw}=0.0574(3600)=207\ \text{m}^3/\text{h}

Engineering Comment

The flow is a utility-header demand, not only an exchanger sizing result. Check header pressure, return-temperature limit, cooling-tower capacity, fouling allowance, seasonal water temperature, and whether other units peak at the same time.

Worked Example 2: Exchanger Area from LMTD

A counterflow exchanger cools a hot stream from $140^\circ\text{C}$ to $90^\circ\text{C}$ while heating a cold stream from $30^\circ\text{C}$ to $70^\circ\text{C}$ . Required duty is $1.80\ \text{MW}$ , estimated $U=650\ \text{W/(m}^2\text{K)}$ , and LMTD correction factor is $F=0.95$ .

Terminal differences:

\Delta T_1=140-70=70\ \text{K}

\Delta T_2=90-30=60\ \text{K}

Log-mean temperature difference:

\displaystyle \Delta T_{lm}=\frac{70-60}{\ln(70/60)}=64.9\ \text{K}

Area:

\displaystyle A=\frac{1{,}800{,}000}{650(0.95)(64.9)}=44.9\ \text{m}^2

Engineering Comment

This is a clean first-pass area. Add fouling resistance, pressure-drop limits, mechanical constraints, cleaning access, corrosion allowance, and minimum approach checks before selecting equipment.

Worked Example 3: Steam Consumption for a Reboiler

A reboiler requires $\dot{Q}=1.20\ \text{MW}$ . The useful enthalpy drop from steam inlet to condensate outlet is estimated as $2100\ \text{kJ/kg}$ . Allow $10\%$ distribution and trap losses.

Base steam rate:

\displaystyle \dot{m}_{steam}=\frac{1200}{2100}=0.571\ \text{kg/s}

Hourly rate:

\dot{m}_{steam}=0.571(3600)=2057\ \text{kg/h}

Including the loss allowance:

\dot{m}_{steam,total}=2057(1+0.10)=2263\ \text{kg/h}

Engineering Comment

The steam pressure must still provide enough saturation temperature and control-valve pressure drop. The calculation also assumes condensate drains freely; flooding a reboiler can reduce heat transfer even when steam mass flow appears adequate.

Worked Example 4: Fouling Duty Shortfall

A clean exchanger has $U_{clean}=850\ \text{W/(m}^2\text{K)}$ . After operation, measurements imply $U_{dirty}=520\ \text{W/(m}^2\text{K)}$ . The required clean-duty case is $1.50\ \text{MW}$ at approximately the same area and temperature program.

Approximate dirty-duty ratio:

\displaystyle \frac{\dot{Q}_{dirty}}{\dot{Q}_{clean}}\approx\frac{520}{850}=0.612

Dirty duty:

\dot{Q}_{dirty}=0.612(1.50)=0.918\ \text{MW}

Duty shortfall:

\Delta \dot{Q}=1.50-0.918=0.582\ \text{MW}

Apparent fouling resistance:

\displaystyle R_{f,app}=\frac{1}{520}-\frac{1}{850}=7.46\times10^{-4}\ \text{m}^2\text{K/W}

Engineering Comment

The duty loss is large enough to affect capacity or downstream utility load. Confirm the diagnosis with pressure-drop trend, hot-side and cold-side heat-balance closure, instrument checks, and product-quality impact before scheduling cleaning.

Worked Example 5: Pumping Power for Cooling-Water Increase

A cooling-water loop must deliver $Q_v=0.060\ \text{m}^3/\text{s}$ through an exchanger and piping path with total pressure drop $\Delta p=180\ \text{kPa}$ . Pump efficiency is $\eta_{pump}=0.70$ .

Hydraulic power:

\dot{W}_{hyd}=180{,}000(0.060)=10{,}800\ \text{W}

Shaft power:

\displaystyle \dot{W}_{shaft}=\frac{10{,}800}{0.70}=15{,}400\ \text{W}=15.4\ \text{kW}

Engineering Comment

If the flow increase is a workaround for fouling, the electrical penalty may continue while heat-transfer performance keeps degrading. Check whether cleaning, revised water treatment, or exchanger retubing is more appropriate than simply increasing pump load.

Worked Example 6: Heat Recovery Fuel Savings

A process-to-process exchanger can recover $\dot{Q}_{rec}=650\ \text{kW}$ for $6000\ \text{h/year}$ . Boiler efficiency is $\eta_{boiler}=0.82$ .

Annual recovered heat:

E_{rec}=650(6000)=3{,}900{,}000\ \text{kWh/year}

Fuel energy avoided:

\displaystyle E_{fuel,avoided}=\frac{3{,}900{,}000}{0.82}=4{,}756{,}000\ \text{kWh/year}

In energy units:

E_{fuel,avoided}=4{,}756\ \text{MWh/year}

Engineering Comment

The energy saving is significant, but the exchanger must still satisfy temperature approach, pressure drop, fouling, corrosion, contamination, startup bypass, and controllability requirements. Heat recovery that destabilizes the process can create more operating cost than it saves.

Common Formula Mistakes

The most common mistake is using one clean-duty point as proof of service capacity. Fouling, viscosity change, vapor generation, maldistribution, bypassing, control-valve position, and pressure drop can reduce useful duty even when nominal area appears adequate.

Another frequent error is mixing process and utility boundaries. Transformer loss, pump power, steam distribution loss, condensate return energy, heat recovery, and exchanger heat loss must be counted only in the boundary where they actually occur.

Steam calculations can mislead when condensate drainage, noncondensables, trap capacity, control-valve authority, superheat, subcooling, water hammer, and exchanger pressure rating are ignored.

Cooling-water calculations can also fail when supply temperature, return limit, cooling-tower approach, water treatment, fouling, seasonal wet bulb, header pressure, and simultaneous users are not included.

Heat recovery is sometimes evaluated only by energy savings. Contamination risk, reliability, pressure drop, startup bypass, cleaning access, corrosion, control interaction, and failure consequence can govern the decision.

Validation Evidence Package

For a process heat-transfer or utility calculation, verify:

the process boundary and sign convention are stated;
heat duties close across hot and cold sides within measurement uncertainty;
property values match temperature, pressure, composition, and phase;
clean, fouled, turndown, startup, seasonal, and abnormal cases are separated;
pressure drop, pump power, valve authority, and cavitation are checked;
steam pressure, condensate drainage, trap capacity, and water hammer risk are reviewed;
cooling-water supply temperature, return limit, treatment, and tower capacity are checked;
fouling trends are monitored with duty, pressure drop, and inspection evidence;
heat recovery is evaluated with operability, contamination risk, and bypass strategy;
safety margins cover loss of cooling, excess heating, blocked-in liquid expansion, and control failure.
instrument calibration, property basis, field data snapshot, control position, and plant operating state are preserved with the calculation.
the release decision states whether the case is clean, fouled, turndown, startup, seasonal, abnormal, or post-cleaning.

REF

Disciplines

Chemical Process Heat Transfer and Utility Systems Formula Sheet

How to Use This Formula Sheet

Basis and Validity Limits

Notation and Unit Basis

Heat Duty

Heat-Exchanger Energy Balance

LMTD Method

Overall Coefficient and Fouling

Effectiveness-NTU Checks

Cooling-Water and Chilled-Water Demand

Steam, Condensate, and Reboiler Duty

Heat Recovery and Utility Savings

Hydraulic and Pumping Power Checks

Utility Header Capacity and Diversity

Control and Safety Margins

Worked Example 1: Cooling-Water Flow for a Product Cooler

Engineering Comment

Worked Example 2: Exchanger Area from LMTD

Engineering Comment

Worked Example 3: Steam Consumption for a Reboiler

Engineering Comment

Worked Example 4: Fouling Duty Shortfall

Engineering Comment

Worked Example 5: Pumping Power for Cooling-Water Increase

Engineering Comment

Worked Example 6: Heat Recovery Fuel Savings

Engineering Comment

Common Formula Mistakes

Validation Evidence Package

See also