Environmental Systems & Mass Balances Workbench

Interactive workspace initializes in your browser. Engineering method, assumptions, validation, and references are available below.

Engineering reference

Environmental Systems: theory, method, and sources

This environmental & energy engineering workspace publishes 9 governing equations, 5 stated assumptions, 1 documented boundary, and 2 sources so the numbers it returns can be checked rather than taken on trust.

Calculations run locallyCalculation & source methodology

How this tool works

Nine modules cover pollutant loading, stream and pipe mixing, hydraulic retention, first-order decay, continuously stirred tank reactors, mass accumulation balances, population projection, screening risk ratios, and operational carbon inventories.

The reactor and mass balance modules share the same first-order rate convention, so a decay constant measured in one context carries directly into the others.

Calculators and topics covered

mass balance
pollution
risk
carbon
pollutant load
CSTR
retention time
environmental mass balance
carbon inventory

Core equations

\text{pollutant load:}\quad L = Q \times C

\text{complete mixing:}\quad C_{\mathrm{mix}} = \frac{Q_{1} C_{1} + Q_{2} C_{2}}{Q_{1} + Q_{2}}

\text{hydraulic retention time:}\quad \mathrm{HRT} = \frac{V}{Q}

\text{first-order decay:}\quad C = C_{0} e^{- kt}

\text{steady-state CSTR:}\quad C_{\mathrm{out}} = \frac{C_{in}}{1 \frac{+ kV}{Q}}

\text{mass accumulation:}\quad \Delta M = \left(\text{input} - \text{output} - \text{reaction}\right) \cdot t

\text{population projection:}\quad P = P_{0} \left(1 + r\right)^{n}

\text{risk quotient:}\quad RQ = \frac{\text{concentration}}{\text{benchmark}}

\text{carbon inventory:}\quad CO_{2} e = \sum \left(\text{activity} \times \text{emission}\; \text{factor}\right)

Method and assumptions

Assumptions

Reactors are assumed completely mixed and at steady state unless the module explicitly integrates over time.
Decay follows first-order kinetics with a single rate constant, independent of temperature and concentration.
Mixing is instantaneous and conservative; sorption, volatilization, and settling are not modelled separately.
Risk quotients are screening indicators only and do not constitute a risk assessment.
Emission factors are user-supplied and must match the region, fuel mix, and reporting year being assessed.

Limitations and design boundaries

Educational screening calculations only. Site design, permitting, compliance, exposure assessment, and lifecycle inventories require verified data, current standards, uncertainty analysis, and qualified professional review.

Sources and references

Primary sources are preferred for ratings, standards, manufacturer data, and externally defined constants.

Source policy

Davis and Masten, Principles of Environmental Engineering and Science
Mihelcic and Zimmerman, Environmental Engineering