Conservation and accounting

Much of engineering is simply careful accounting of things other than money. The accountings are called mass balances, energy balances, component balances, momentum balances. 

This general balance equation and its variants form the basis of much of chemical engineering. If the creation and destruction terms are zero, then it is called a conservation equation. If they are not zero then Eq. 2.1 has no common name, but is widely used, for example, with chemical reactions, where it allows us to compute the changes in various chemicals as a chemical reaction destroys one species and creates another. Remember that it applies only to a system with properly defined boundaries. All balances can be changed to rate equations by dividing both sides by some time interval, dt  

Physical and Chemical Equilibrium for Chemical Engineers, Second Edition. Noel de Nevers. 2012 John Wiley Sons, Inc. Published 2012 by John Wiley Sons, Inc. 

FIGURE 2.1 The system boundaries divide the whole universe into two parts the system and the surroundings. 

One also sees this equation and its later variants in the form 

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There are a number of limitations in interface capturing schemes that continue to be addressed by researchers. One is the problem of so-called parasitic or spurious currents [6] which can be attributed to the interfacial regions being underresolved. These currents can be reduced via formulations that strictly enforce energy conservation and account for exchanges of kinetic and surface energies [11]. There are also difficulties in computations at small values of surface tension when the computed objects (drops, filaments, bubbles) become very small and cannot be... 

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