Formula sheet

Chemical Process Calculations Formula Sheet

Chemical process formulas for mass balances, component balances, conversion, yield, residence time, heat duty, heat exchangers, flow, valves, and reactors.

Branch: Chemical Engineering
Content: Formula sheet
Updated: May 29, 2026
Revision: v1.0.8 · reviewed

This formula sheet collects common first-pass calculations for chemical process balances, reactors, flow systems, and heat-transfer checks. It is intended for screening, design review, troubleshooting, and consistency checks. Detailed design still requires verified physical properties, reaction data, governing standards, safety review, and plant-specific assumptions.

Use a consistent basis. State whether flows are mass, molar, or volumetric; whether the process is steady or transient; whether composition is mass fraction or mole fraction; and whether the stream is liquid, vapor, gas, solid, slurry, or multiphase.

Total mass balance

General balance:

\text{accumulation}=\text{in}-\text{out}+\text{generation}-\text{consumption}

For total mass in ordinary processes, generation and consumption are normally zero:

\displaystyle \frac{dm}{dt}=\sum \dot{m}_{in}-\sum \dot{m}_{out}

At steady state:

\displaystyle \sum \dot{m}_{in}=\sum \dot{m}_{out}

Mass flow from density and volumetric flow:

\dot{m}=\rho Q

Volumetric flow from average velocity:

Q=vA

These equations require consistent units and density values appropriate to temperature, pressure, composition, and phase.

Component balance

For component $i$ in molar terms:

\displaystyle \frac{dn_i}{dt}=\sum \dot{n}_{i,in}-\sum \dot{n}_{i,out}+R_i

At steady state:

\displaystyle 0=\sum \dot{n}_{i,in}-\sum \dot{n}_{i,out}+R_i

For a well-mixed volume $V$ with rate of formation $r_i$ :

R_i=r_iV

For species consumed by reaction, $r_i$ is negative under the common sign convention. State the sign convention before using reaction-rate terms.

Mole and mass fractions

Mole fraction:

\displaystyle y_i=\frac{n_i}{\sum n_i}

Mass fraction:

\displaystyle w_i=\frac{m_i}{\sum m_i}

Mass from moles:

m_i=n_iM_i

where $M_i$ is molecular weight.

Average molecular weight of a mixture from mole fractions:

\displaystyle \bar{M}=\sum y_iM_i

Do not mix mole fraction and mass fraction without conversion.

Conversion, yield, and selectivity

Conversion of reactant $A$ :

\displaystyle X_A=\frac{F_{A0}-F_A}{F_{A0}}

Outlet reactant flow from conversion:

F_A=F_{A0}(1-X_A)

Yield of desired product $P$ on reactant $A$ basis:

\displaystyle Y_{P/A}=\frac{\text{moles of }P\text{ formed}}{\text{moles of }A\text{ fed or consumed}}

Selectivity of desired product $P$ over undesired product $U$ :

\displaystyle S_{P/U}=\frac{\text{moles of }P\text{ formed}}{\text{moles of }U\text{ formed}}

Always state whether yield is based on feed, converted reactant, theoretical product, mass, or moles.

Reactor residence time

Nominal residence time for a liquid reactor:

\displaystyle \tau=\frac{V}{Q}

Space time for an inlet volumetric flow rate $Q_0$ :

\displaystyle \tau=\frac{V}{Q_0}

Space velocity:

\displaystyle SV=\frac{Q_0}{V}

For gas-phase systems, volumetric flow can change significantly with temperature, pressure, and moles. State whether $Q$ is inlet, outlet, actual, or standard volumetric flow.

Ideal CSTR design equation

For a steady-state, well-mixed CSTR with one reaction and species $A$ :

F_{A0}-F_A+ r_A V=0

If $-r_A$ is the positive rate of disappearance of $A$ :

\displaystyle V=\frac{F_{A0}X_A}{(-r_A)_{exit}}

The rate is evaluated at reactor exit composition and temperature because a CSTR is assumed well mixed.

Ideal plug-flow reactor equation

For an ideal PFR:

\displaystyle \frac{dF_A}{dV}=r_A

Using conversion:

\displaystyle V=F_{A0}\int_0^{X_A}\frac{dX}{-r_A}

The rate varies along the reactor as concentration, temperature, pressure, and phase conditions change. Nonisothermal PFRs require simultaneous material and energy balances.

First-order reaction checks

For a constant-volume batch reactor with first-order consumption of $A$ :

C_A=C_{A0}e^{-kt}

Conversion:

X_A=1-e^{-kt}

For a first-order ideal CSTR with constant density:

\displaystyle X_A=\frac{k\tau}{1+k\tau}

For a first-order ideal PFR with constant density:

X_A=1-e^{-k\tau}

These formulas are screening equations. Real kinetics may depend on temperature, catalysts, inhibition, equilibrium, mass transfer, or side reactions.

Heat duty

Sensible heat duty:

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

Heat duty with phase change:

\dot{Q}=\dot{m}\Delta h

Reaction heat release or absorption, using extent rate $\dot{\xi}$ :

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

Sign conventions vary. State whether positive heat is into or out of the process.

Heat exchanger equation

Overall heat-transfer relation:

\dot{Q}=UA\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)}

Thermal resistance form:

\displaystyle \frac{1}{U}=\frac{1}{h_i}+R_{wall}+R_{fouling}+\frac{1}{h_o}

This simplified resistance equation omits geometry factors. Use the correct cylindrical or plate geometry for detailed design.

Reynolds number and flow regime

Reynolds number for pipe flow:

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

where $\rho$ is density, $v$ is average velocity, $D$ is hydraulic diameter for simple pipe flow, and $\mu$ is dynamic viscosity.

Laminar pipe flow is commonly associated with:

Re<2300

Turbulent pipe flow is commonly associated with:

Re>4000

The transition region is system-dependent. In process equipment, fittings, roughness, mixing, non-Newtonian behaviour, multiphase flow, and pulsation can shift practical behaviour.

Pressure drop and valves

Pressure drop due to flow resistance is often estimated from a friction relation:

\displaystyle \Delta P=f\frac{L}{D}\frac{\rho v^2}{2}

Minor losses:

\displaystyle \Delta P=K\frac{\rho v^2}{2}

Valve flow coefficient relationships depend on unit system and standard. Conceptually, valve capacity increases with opening and pressure drop, but liquid flashing, cavitation, gas expansion, choking, viscosity, and two-phase flow can invalidate simple estimates.

For design review, check normal flow, minimum controllable flow, maximum flow, startup, shutdown, fail position, pressure rating, temperature rating, and relief cases.

Vapor pressure and flashing check

A liquid can flash or cavitate when local pressure approaches or falls below vapor pressure:

P_{local}\leq P_{vap}(T)

This check is important near pump suction, control valves, orifices, hot liquid lines, relief systems, and vacuum equipment.

Vapor pressure is strongly temperature-dependent. Use property data at the actual process composition and temperature, especially for mixtures.

Efficiency and utility checks

Thermal efficiency:

\displaystyle \eta=\frac{\text{useful energy output}}{\text{energy input}}

Heat recovered fraction:

\displaystyle \eta_{rec}=\frac{\dot{Q}_{recovered}}{\dot{Q}_{available}}

Utility demand for a heating or cooling service:

\displaystyle \dot{m}_{utility}=\frac{\dot{Q}}{\Delta h_{utility}}

These estimates support steam, cooling water, chilled water, refrigerant, heat-transfer oil, and waste-heat recovery calculations.

Scale-up checks

Volume of a cylindrical vessel:

\displaystyle V=\frac{\pi D^2}{4}H

Surface area available for jacket heat transfer scales roughly with:

A \propto D^2

Volume scales roughly with:

V \propto D^3

This is why heat removal can become harder at larger scale. Reactor scale-up must check mixing, heat transfer, mass transfer, residence-time distribution, pressure drop, and relief requirements.

Practical checklist

Use these formulas with a short process-calculation checklist:

Draw the boundary before writing equations.
Choose mass, molar, or volumetric basis and keep it consistent.
Close total and component balances.
State reaction stoichiometry and sign convention.
Check conversion, yield, selectivity, recycle, and purge.
Add heat duty and heat-transfer limits.
Check flow regime, pressure drop, valves, and vapor pressure.
Review startup, shutdown, abnormal operation, and relief cases.
Compare calculations with measurements, pilot data, or a second independent estimate.

The equations are only as good as the assumptions behind them. Property data, kinetics, phase behaviour, fouling, control dynamics, and safety limits usually determine whether a process design is actually usable.

REF

Disciplines