massabalance

Mass balance is a bookkeeping method based on the law of conservation of mass. It is applied to any system defined by a control volume, where material can enter, leave, accumulate, or be produced or consumed inside.

Let M denote the total mass within the control volume. The rate of change of M is equal to the sum of all inflows minus the sum of all outflows plus internal sources minus internal sinks: dM/dt = Σṁ_in − Σṁ_out + ṁ_source − ṁ_sink. For a single species or when there are no internal sources or sinks, this reduces to accumulation = inflow − outflow. In steady state, dM/dt = 0 and inflows equal outflows.

The control-volume mass balance is widely used in chemical engineering, environmental modeling, hydrology, and geosciences. It underpins the design and analysis of systems where materials move and transform. Examples include the design of chemical reactors, wastewater treatment, air and water quality assessments, and the water balance of a watershed. In glaciology, glacier mass balance tracks accumulation and ablation to estimate changes in ice volume.

Mass balance calculations can track the total mass of all phases together or follow individual species, depending on the problem. Key considerations include correctly defining system boundaries, accounting for phase changes and density variations, handling multi-phase flows, and recognizing measurement uncertainties. Mass balance is distinct from energy balance, though both are often used together in process analysis.