Mass balance
By accounting for material entering and leaving a system, mass flows can be identified which might have been unknown, or difficult to measure without this technique.
For example, mass balance theory is used to design chemical reactors, to analyse alternative processes to produce chemicals, as well as to model pollution dispersion and other processes of physical systems.
Mass balances form the foundation of process engineering design.
These techniques are required for thorough design and analysis of systems such as the refrigeration cycle.
Strictly speaking the above equation holds also for systems with chemical reactions if the terms in the balance equation are taken to refer to total mass, i.e. the sum of all the chemical species of the system.
However, if this is not the case then the mass balance equation must be amended to allow for the generation or depletion (consumption) of each chemical species.
Some use one term in this equation to account for chemical reactions, which will be negative for depletion and positive for generation.
However, the conventional form of this equation is written to account for both a positive generation term (i.e. product of reaction) and a negative consumption term (the reactants used to produce the products).
This modified equation can be used not only for reactive systems, but for population balances such as arise in particle mechanics problems.
Solids are collected at the bottom by means of a conveyor belt partially submerged in the tank, and water exits via an overflow outlet.
The tank is assumed to be operating at steady state, and as such accumulation is zero, so input and output must be equal for both the solids and water.
In these systems output streams are fed back into the input of a unit, often for further reprocessing.
[2]: 97–105 Such systems are common in grinding circuits, where grain is crushed then sieved to only allow fine particles out of the circuit and the larger particles are returned to the roller mill (grinder).
The differential mass balance is usually solved in two steps: first, a set of governing differential equations must be obtained, and then these equations must be solved, either analytically or, for less tractable problems, numerically.
[4]: 40–41 Many chemistry textbooks implicitly assume that the studied system can be described as a batch reactor when they write about reaction kinetics and chemical equilibrium.
where In a fed-batch reactor some reactants/ingredients are added continuously or in pulses (compare making porridge by either first blending all ingredients and then letting it boil, which can be described as a batch reactor, or by first mixing only water and salt and making that boil before the other ingredients are added, which can be described as a fed-batch reactor).
In the first example, we will show how to use a mass balance to derive a relationship between the percent excess air for the combustion of a hydrocarbon-base fuel oil and the percent oxygen in the combustion product gas.
where wC, wH, wS, wO refer to the mass fraction of each element in the fuel oil, sulfur burning to SO2, and AFRmass refers to the air-fuel ratio in mass units.
In the second example, we will use the law of mass action to derive the expression for a chemical equilibrium constant.
Assume we have a closed reactor in which the following liquid phase reversible reaction occurs:
According to the law of mass action the forward reaction rate can be written as
[4]: 41 A lake can be regarded as a tank reactor, and lakes with long turnover times (e.g. with low flux-to-volume ratios) can for many purposes be regarded as continuously stirred (e.g. homogeneous in all respects).
We can thus draw the conclusion that reaction rate can not be defined in a general manner using
without mentioning that this definition implicitly assumes that the system is closed, has a constant volume and that there is only one reaction.
When a mass balance is made for a tube, one first considers an infinitesimal part of the tube and make a mass balance over that using the ideal tank reactor model.
[4]: 46–47 That mass balance is then integrated over the entire reactor volume to obtain:
In numeric solutions, e.g. when using computers, the ideal tube is often translated to a series of tank reactors, as it can be shown that a PFR is equivalent to an infinite number of stirred tanks in series, but the latter is often easier to analyze, especially at steady state.
A different reactor model might be needed for the energy balance: A system that is closed with respect to mass might be open with respect to energy e.g. since heat may enter the system through conduction.
In industrial process plants, using the fact that the mass entering and leaving any portion of a process plant must balance, data validation and reconciliation algorithms may be employed to correct measured flows, provided that enough redundancy of flow measurements exist to permit statistical reconciliation and exclusion of detectably erroneous measurements.
Software packages exist to make this commercially feasible on a daily basis.
