Massbalance

Mass balance, also called material balance, is a calculation framework used to track the quantity of matter as it flows through a system, based on the conservation of mass. It is widely used in engineering and environmental science.

In a control volume, the mass balance for a species i is dM_i/dt = ∑m_in,i - ∑m_out,i + generation_i - consumption_i. For overall mass (i.e., all species together) it's dM/dt = ∑m_in - ∑m_out. At steady state, dM/dt = 0, so total incoming mass equals total outgoing mass.

Systems can be open (mass crosses the boundary) or closed (no net mass transfer). When chemical reactions occur within the system, generation and consumption terms appear, and species masses relate via stoichiometry rather than independent balances.

There are two common forms: an overall mass balance for the entire system; and component or species balances for individual substances. The principle can be extended to dynamic (transient) and steady-state analyses. Phase changes may complicate the mass in/out terms.

Applications include chemical process design, wastewater treatment, combustion, environmental impact assessments, and process control. A simple example: a tank with inflow ṁ_in and outflow ṁ_out has dM/dt = ṁ_in - ṁ_out; at steady state ṁ_in = ṁ_out.

Practical considerations include measurement accuracy, mixing assumptions, density changes, and the need to account for leaks or side streams. Mass balance is foundational in process modeling and material accounting.